The surprise winner snapped a 75-race losing streak in the series with his third career Sprint Cup victory. Vickers drives a part-time schedule for Michael Waltrip Racing and competed in just his eighth race of the season.
Kyle Busch was second and Jeff Burton third. Pole winner Brad Keselowski was fourth and Aric Almirola fifth.
Jimmie Johnson brushed off his 43rd-place start to finish sixth. Tony Stewart was running inside the top 10 at the final caution until he ran out of fuel and plummeted to 26th.
Vickers hadn't won since the August 2009 race at Michigan. He won his first career Cup race in August 2006 at Talladega Superspeedway.
MWR fields cars for Martin Truex Jr. and Clint Bowyer. But the No. 55 has been shared this season among Vickers, Mark Martin and Michael Waltrip.
“He does a good job for us, all of our guys do,” crew chief Rodney Childers said.
Vickers' win may have put him in position for a full-time ride at MWR in 2014.
Busch and Vickers finished 1-2 in Saturday's Nationwide Series race. Both drivers had to stretch their fuel and Vickers ran out just as he crossed the finish line.
He was in a similar spot again down the stretch a race later. He had just enough to zip past Stewart with 13 laps left and didn't run out until it was time for the celebratory burnout.
Stewart wasn't so lucky a week after he finished second at Daytona.
Johnson, who won at Daytona, was mired in last place for the first time in his career after his car flunked post-qualifying inspection. For the five-time Cup champ, that was no big deal. The points leader made quick work through the back of the field and worked his way up to the front for most of the race.
He easily breezed past 71-year-old Morgan Shepherd, the oldest driver to start a race in NASCAR's Sprint Cup series.
Kurt Busch led a race-high 102 laps before he connected with Ryan Newman to end his shot at his first victory of the season. Off the restart, Danica Patrick was involved in a three-car wreck that included boyfriend Ricky Stenhouse Jr.
“We're all bunched up on those restarts,” Patrick said. “I'm not sure if I misjudged the breaking zone or they stopped really quick in front of me.”
Vickers survived it all to win for the third time in 271 Sprint Cup races.
Driving for Red Bull Racing, his career was seriously derailed in 2010 because of clots in his leg and lungs. He had two procedures to close a hole in his heart and insert a stent into a vein in his left leg.
After Red Bull shut down after the 2011 season, Vickers was hooked on with MWR. He's been driving full-time this season in the Nationwide Series for Joe Gibbs Racing.