"I don't think we should be resting on anything because we haven't accomplished anything yet," Quenneville said.
"We don't want to get ahead of ourselves and feel good [where] maybe we think we're better than we are."
The Hawks played their 27th game Friday night, facing the Colorado Avalanche at the Pepsi Center, and they entered it in search of their 35th point.
They didn't reach the 35-point mark until the 34th game in each of the previous two seasons, during which they failed to reach the postseason.
The Hawks did indeed reach 35 points as they recorded a 4-3 victory over the Avalanche. The victory extended the Hawks' winning streak to three and their points streak to five (4-0-1) and improved their road record to 5-5-3 and their overall mark to 14-6-7.
Dustin Byfuglien's second goal of the game, shortly after a power play had expired, provided the winning margin with 6 minutes 9 seconds to play.
Andrew Ladd had tied it 3-3 midway through the third when he converted a feed from Dave Bolland. Wojtek Wolski's goal 3:43 into the third had put Colorado up.
Craig Adams got the Hawks off to a good start, scoring 2:31 into the game. The veteran picked up a rebound of his own shot and rifled a shot from between the circles past Avalanche goaltender Peter Budaj. The goal was the first of the season for Adams in 14 games and his first since March 29 against the St. Louis Blues.
Colorado evened the score 1-1 on Chris Stewart's goal midway through the first period. Stewart's blast from the top of the right circle got by Hawks goalie Nikolai Khabibulin and came four seconds after the Avalanche had completed a power play when Kris Versteeg was sent off for goaltender interference.
Ian Laperriere's goal with just less than six minutes remaining in the opening period gave the Avalanche a 2-1 lead. Teammate John-Michael Liles sent a shot toward the Hawks net that Laperriere redirected past Khabibulin.
Khabibulin was making his first start since suffering a lower-body injury Nov. 26 against the Sharks in San Jose. Cristobal Huet had been in net for the Hawks' last six games.
The Hawks had a chance to tie the game in the opening minute of the second period when they had a two-man advantage. But they couldn't cash in during the initial stages of the power play and then saw it negated when they took a penalty for too many men on the ice.
A bit later in the period the Hawks did tie it 2-2 when Jonathan Toews made a pass to spring Byfuglien on a breakaway. Budaj got a piece of Byfuglien's attempt from in close, but the puck got through him for the winger's fourth goal of the season.
The Hawks controlled the puck in the Avalanche zone for much of the second period, had the better of the scoring chances and outshot Colorado 7-3. But they couldn't solve Budaj again.