With his team leading 1-0, Calgary center Joe Colborne was whistled for his second penalty of the game 3:26 into the second for holding.
Ducks forward Jakob Silfverberg recollected the puck on the power play, dished a backhanded pass and Ryan Kesler blasted a shot past Flames goalie Karri Ramo on the power play 4:59 into the second, making the score 1-1.
Kesler's goal was his fifth of the playoffs.
Calgary quickly responded as forward Johnny Gaudreau slammed a rising shot past Ducks goalie Frederik Andersen on his team's first shot of the period at 5:55 of the second, for a 2-1 lead.
Gaudreau, born on August 3, 1993, was 12 years old the last time the Flames won in Anaheim on April 25, 2006.
Kesler drew a questionable double-minor high-sticking call at 8:18 of the first period for jamming Calgary center Sean Monahan to the boards.
The Flames capitalized with the extra two minutes of penalty time, as Jiri Hudler fired a power-play shot past Ducks defenseman Francois Beauchemin and Andersen to the net 10:43 into the game -- and 2:24 into the penalty -- for a 1-0 Calgary lead.
The Ducks had quite a scare late in the second when NHL playoff points leader Perry was decked to the ice by a hit from Calgary center Matt Stajan. Perry tried to get up, held his right knee area and fell back down before being aided to the dressing room with 4:11 left.
Yet, Perry returned to the game with 1:01 remaining in the second.
Offensive pressure amplified in the final minute, leaving the hosts with a 26-14 shots advantage at the horn.
Matt Beleskey stoned by Ramo off a long pass from goalie Frederik Andersen that set up a one-on-one.
Series over 2:26 in, though, on a Corey Perry goal, pushing it past Ramo.
To answer the shots' disparity, Calgary has blocked 25 Anaheim shots while the Ducks have just nine in the category.
In an equal hitting contest, Ryan Kesler and defenseman Clayton Stoner leads the hosts with five apiece.
Anaheim is winning the faceoff battle, 40-24.
Ducks 2, Calgary Flames 2 (end of third period)
We're going to overtime in Game 5.
The Ducks and Flames are tied, 2-2, with Anaheim dominating the shots counter, 40-19.
Both teams had late chances. Matt Beleskey whiffed at an opening in the final 10 seconds and Calgary's Matt Stajan concluded a rush by missing a shot wide.
This is the second overtime game of the series. Calgary won Game 3 in overtime.
A Kyle Palmieri takeaway and shot forces a faceoff next to the Calgary net with 5:43 left in the third. A timeout leads to mass orange towel waving in the building where the Ducks have dominated Calgary.
A Ryan Getzlaf shot is blocked by the Flames.
Ducks Coach Bruce Boudreau, trying to guide his first team to a conference final, calls timeout with 4:11 left in the third, before a faceoff to the right of his goalie Frederik Andersen.
There's less than three minutes left in regulation.
The Ducks' shots advantage in the third is 12-1, and they withstand chances by Johnny Gaudreau and a wide one from Dennis Wideman.
Ducks captain Ryan Getzlaf misses high with less than nine minutes left in the third. Timeout with 8:13 left.
More pressure from the Ryan Kesler line and the Ducks have 31 shots to Calgary's 15 at the 4:41 mark of the third.
In the playoffs, the Ducks are 3-0 when trailing after two periods.
A Corey Perry shot is knocked down. An Andrew Cogliano try is saved. The disparity is now 36-15.
Ducks 2, Calgary Flames 2 (19:01 left in third period)
On the power play to start the third period, the comeback-savvy Ducks tied the score, 2-2, with forward Matt Beleskey breaking a team playoff record with a goal in his fifth consecutive game.
At 59 seconds, Beleskey deflected in a blue-line shot from Francois Beauchemin.
Calgary Flames 2, Ducks 1 (end of second period)
Cory Perry returned to the game with 1:01 remaining in the second.
Offensive pressure by Ryan Kesler, Jakob Silfverberg and Simon Despres amplified in the final minute, leaving the hosts with a 26-14 shots advantage at the horn.
Calgary's Mikael Backlund picked up a slashing penalty as time expired, giving the Ducks a full power play when the third period begins.
After two, Calgary leads the Ducks, 2-1.
Anaheim has 29 comeback victories this season, including 21 after trailing in the third period.
The Flames had no shots during the Hampus Lindholm penalty and have managed just three shots thus far.
Now, Corey Perry has been decked by a hit from Calgary center Matt Stajan. Perry tried to get up, held his right knee area and fell back down before being aided to the dressing room with 4:11 left in the second.
Perry started the night leading the NHL in playoff points (14) with six goals.
Two scuffles, involving Ducks Patrick Maroon and Clayton Stoner defending their star teammate, ensued along with roughing penalties.
Perry returned to the bench area within three minutes of game time.
Calgary's Johnny Gaudreau, born on August 3, 1993, was 12-years-old the last time the Flames won in Anaheim.
Tomas Fleischmann whiffed on a rebound try to Karri Ramo's right on what was the Ducks' 20th shot on goal.
At the 11:32 mark of the second, Anaheim's shots advantage was 22-12.
But the Flames remained pesky, with Dennis Wideman tipping away a Corey Perry pass from the side of the goal to center ice, where a Duck was moving toward a shot.
And now with 7:03 left in the second, it's still 2-1 Flames, with Hampus Lindholm getting tagged with a cross-checking penalty.
Calgary Flames 2, Ducks 1 (14:05 left in second)
Calgary quickly responded, Johnny Gaudreau scoring on his team's first shot of the period, 5:55 into the second, for a 2-1 lead. Jiri Hudler and Dennis Wideman had the assists.
Ducks 1, Calgary Flames 1 (15:01 left in second)
Calgary's Joe Colborne was whistled for his second penalty 3:26 into the second for holding.
Flames goalie Karri Ramo knocked down a Jakob Silfverberg shot with Ryan Kesler providing a screen.
But after Matt Beleskey lost grip of the puck, Silfverberg collected it again, dished a backhanded pass and Kesler blasted a shot past Ramo on the power play 4:59 into the second, making the score 1-1.
Kesler's goal was his fifth of the playoffs.
Fowler had the secondary assist.
Part of the reason for the Ducks' scoreless first period was Calgary defenseman Dennis Wideman's five blocked shots, emphasizing one of the visitors' strengths.
Anaheim forward Jakob Silfverberg led his team in ice time (7:54) in the first, delivering two hits.
The Ducks, working with 29 seconds of power-play time to start the frame, crashed toward Flames goalie Karri Ramo in the opening seconds of the second, but were denied. A faceoff got away and Patrick Maroon couldn't grip a pass and the penalty was killed.
Calgary Flames 1, Ducks 0 (end of first period)
The Ducks had a power-play opportunity less than a minute after falling behind after Calgary's Joe Colborne committed interference by shoving Ducks defenseman Hampus Lindholm to the post right of Andersen.
But Anaheim failed to significantly pressure Karri Ramo with the extra man and the penalty was killed.
Then, Ducks forward Jakob Silfverberg slid a pass to the crease that Kesler couldn't find, and Anaheim defenseman Simon Despres committed a holding penalty with 3:38 left in the first.
Ramo denied Andrew Cogliano on a short-handed try seconds later, then Andersen stopped Colborne up close right before Calgary's Kris Russell shot wide as the penalty was killed.
Flames forward Johnny Gaudreau then quickly was saddled with a hooking penalty while jostling with Ducks defenseman Sami Vatanen.
A Fowler shot was stopped by a Ramo leg pad and Lindholm was denied with a glove. The first period ended, with Anaheim trailing 1-0, tallying 12 shots on goal to Calgary's nine.
There are 29 seconds remaining on the Ducks' power play when the second period begins.
Calgary Flames 1, Ducks 0 (9:17 left in first period)
Ducks center Ryan Kesler drew a dubious double-minor high-sticking call at 8:18 of the first period for jamming Calgary center Sean Monahan to the boards.
Calgary capitalized with the extra time, as Jiri Hudler fired a power-play shot past Ducks defenseman Francois Beauchemin and Andersen to the net 10:43 into the game -- and 2:24 into the penalty -- for a 1-0 Calgary lead.
It was the Flames' fourth shot on goal.
Game 5 is underway between the Ducks and Calgary Flames at Honda Center.
Enlivened by a band playing in the upper deck in pregame warmups and Metallica's "Enter Sandman" blaring at puck drop, the raucous sellout crowd intends to keep the home team's energy high as it works to avoid a Game 6 return trip to Calgary on Tuesday.
Early on, Ducks defenseman Cam Fowler was stopped at the right post by Calgary goalie Karri Romo while the visitors managed just two shots on goal at Ducks goalie Frederik Andersen in the first 6 minutes, 11 seconds.
It's scoreless with just over 13 minutes left in the first period.
The Ducks tonight seek their first visit to the Western Conference Finals since their Stanley Cup-winning season of 2007, when they meet the Calgary Flames in Game 5 of the conference semifinals at Honda Center.
The Times will provide continued updates throughout the game here.
The chips are stacked in Anaheim's favor considering the top-seeded Ducks are 7-1 in the playoffs, 4-0 at home and have dominated the Flames in Orange County, winning every meeting since April 25, 2006.
Since the Chicago Blackhawks have already earned their way to a third consecutive conference-final series, the Ducks are itching to close the series now and wait for the NHL schedulers to assign their next game instead of a Game 6 in Canada on Tuesday.
A year after his team lost Game 7 of the Western Conference semifinals at home to the eventual-champion Kings, Ducks defenseman Cam Fowler said great teams understand how to close a series.
"Whenever you have this opportunity, you want to make the most of it right away because as beautiful as Calgary is," Fowler said.
"You want to try and avoid those extra games. At the same time, you know the type of team you're dealing with and any sort of life they have, any sort of confidence they can gain, that's pretty dangerous, especially at playoff time. So when you have these opportunities you try to make the most of them.
"I think you'll see a focused group from us."
Ducks forward Matt Beleskey has scored a goal in each game of this series and right wing Corey Perry has six goals and 14 points this postseason.
Ducks center Ryan Getzlaf said the critical element of winning is, "We've got to go out and again win the walls. If we win the walls and get pucks in and get pucks out, we should be fine."
Getzlaf is marking his 30th birthday Sunday, and said he'd like to celebrate with a victory.
"Any time you have a team that feels doubt in any way, you want to put that right back in their heads," Getzlaf said. "So if you can get out to a good start ... the way we want to play."
He said home-ice advantage is at play.
"It's been a good building for us over the last years," Getzlaf said. "We want to maintain that. We don't want anyone to ever come into our building and think they can win, especially in the playoffs."