Kyle Busch was second and Jeff Burton third. Pole winner Brad Keselowski was fourth and Aric Almirola fifth.
Jimmie Johnson, penalized after his car failed a post-qualifying inspection, 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.
"It wasn't until the end when we started running down the 18 [Busch] and the 14 [Stewart] that I felt we had a car capable of winning," Vickers said. "Then I was hungry."
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.
Vickers' win may have put him in position for a full-time ride at MWR in 2014.
"Nothing is a guarantee in life. I learned the hard way," he said. "Even when you think it's done, it's not done. But it definitely goes a long way."
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.
Sprint Cup standings
1. J. Johnson 696
2. C. Bowyer 640 -56
3. C. Edwards 623 -73
4. K. Harvick 622 -74
5. D. Earnhardt Jr. 578 -118
6. M. Kenseth 576 -120
6. Kyle Busch 576 -120
8. G. Biffle 545 -151
9. B. Keselowski 529 -167
10. K. Kahne 523 -173
11. M. Truex Jr. 521 -175
12. J. Gordon 521 -175