Driver Tony Stewart performs a burnout after he won a NASCAR Sprint Cup Series auto race, Sunday, June 2, 2013, at Dover International Speedway in Dover, Del.

DOVER, Del. - Tony Stewart made a late outside pass on Juan Pablo Montoya and held on Sunday at Dover International Speedway to snap a 30-race winless streak.

Stewart hadn't even had a top-five finish this season and was stuck in 20th in the points standings. He took the lead with the pass with three laps left in the 400-mile race.

Stewart hadn't won on the concrete mile track since he swept both Cup races in 2000.

"Our guys at our shop have been digging," Stewart said. "None of these guys get down. We have been down but they haven't gotten down. That is what carries you to days like today at the end of the day."

Seven-time Dover winner Jimmie Johnson appeared to have the car to beat, but jumped a restart and had to serve a pass-through penalty. Johnson argued over the radio and stayed on the track before he finally hit pit road.

With Johnson out of the picture, Montoya and Stewart battled for the lead the rest of the race.

Jeff Gordon was third, followed by Kyle Busch and Brad Keselowski. NASCAR said Keselowski failed post-race inspection because the entire front of his No. 2 Ford was too low.

Stewart's team erupted in celebration in the pits after winning for the first time since last July in Daytona. It was his 48th career win. He hadn't finished better than 20th in his last four races at Dover.

He might not have gotten this one had Johnson not been penalized with about 19 laps left. Johnson jumped ahead of Montoya out of the restart box and NASCAR quickly threw the black flag.

"We certainly had the winning car," Johnson said. "We'll have to come back and do it in the fall."

Montoya's only two career Cup victories came on road courses. He tried to play the spoiler after Johnson's penalty but just didn't have enough to hold off a hard-charging Stewart.

Johnson, who kept the points lead, finished 17th.

"He just wanted to get the jump on me," Montoya said. "He just jumped it too much. I would have tried to do the same."

Matt Kenseth and Martin Truex Jr., both in the top 10 in points entering the race, made early exits because of engine issues.

Pole sitter Denny Hamlin finished 34th after he hit the wall late in the race. Hamlin needed a big points day to try and crack the top 20 if he has any hope at a Chase for the Sprint Cup championship wild-card berth. Hamlin is 26th in the standings, 122 points out of 10th and 74 points out of 20th.

Stewart aided his cause in a wild-card spot with the win. The two drivers in the 11th to 20th spot in the points standings with the most wins earn a spot in the Chase.

"It's been such a tough year," Stewart said.

It got a little easier Sunday. Stewart tested at Dover and hoped that would help at a track that's given him fits the last few years. Stewart-Haas Racing appeared to turn a corner last week at Charlotte after Ryan Newman finished sixth and Stewart was seventh.

Stewart said one strong weekend wasn't going to cure all of SHR's problems.

Make it two and with a big win in hand.

"We got two weeks of momentum under our belt now at two totally different race tracks," Stewart said. "That is big. Momentum is huge in this sport. We still got a lot of work to do. We won't sit."