Kenseth led the final 32 laps Sunday to win for the second time this season. He also won at Texas and became the third driver to win twice this season.
Mark Martin was second and Marcos Ambrose third. Kyle Busch and Brian Vickers rounded out the top five. Busch was forced to start in the rear of the field because of an engine change.
Kenseth made his Cup debut at Dover in 1998 as a fill-in for Bill Elliott.
The 400-mile race was dominated by long stretches of green flag racing. Jimmie Johnson led a race-high 207 laps and finished ninth.
Martin stayed on the track to take the lead when the caution flag came out with 39 laps left. Kenseth made a quick stop and opted for two tires instead of four, the right number for him to pull pass Martin on the restart and then pull away for the victory.
"We were going to do four, we got in the stall and decided to do two. That was the key," Kenseth said.
Kenseth said he was having trouble during the green flag racing because the rubber that built on the track made the concrete slick - an obstacle for a loose car.
When the short runs started coming, Kenseth found a cleaner track and clean air was enough to spark his run.
Kenseth, the 2003 series champion, won his 20th career Cup race. Martin earned his first top-five of the season.
"Today, we finally got a finish," he said. "It looked like we were going to get 15th again with a really fast race car. We've had a race car this good a lot this year. But it seems like for some reason or another we end up in the back of the back."
Johnson and Edwards turned this into a two-car battle for first for the majority of the race. Edwards led 117 laps before falling to seventh place.
Regan Smith was 34th a week after he shocked the sport with his first career win at Darlington Raceway.
Busch and Kevin Harvick had no incidents after a pit road dustup at Darlington landed them on probation. Harvick was 10th.