The 22-year-old Logano rallied past the 53-year-old Martin for a tight finish in the first 400-mile Cup race at Pocono. Pocono shortened the race by 100 miles this season.
Logano's only previous career Cup victory was a rain-shortened win at New Hampshire. Logano had the top car all weekend, posting the fastest practice time Friday and then taking the pole Saturday.
Tony Stewart was third, Jimmie Johnson fourth and Denny Hamlin fifth.
Logano, once a much-hyped phenom when he broke in with Joe Gibbs Racing, was under pressure to produce victories in the final year of his four-year contract.
Logano's win continues a recent uptick of solid results in the Cup series. He has insisted this season his contract status has not added pressure.
But in Victory Lane, he hoped the victory sent a message to his critics.
"I hope it shuts them all up," he said. "It means a whole lot."
At a track known for its tedious 500-mile race, 400 miles was the perfect length to produce a fantastic finish on fresh asphalt on the 2½-mile track.
Martin, one of Logano's earliest supporters, took the lead with eight laps left. Logano, though, bumped Martin out of the way and zipped past for the winning move with three laps remaining.
"I'd call that a bump-and-run," Martin said. "It has been acceptable in this racing for a long time. It's not how I would have done it. Certainly, had I had a fast enough car, he would have gotten a return."
Martin saw Logano race at 11 years old and raved about his potential as future Cup champion. Logano was so full of promise, he was dubbed "Sliced Bread." As in, greatest thing since ...
Logano finished a season-high eighth in the Cup race at Dover last week and now has three top-10s in his last four starts. It could be a sign that things are finally falling into place in his first season with crew chief Jason Ratcliff.
Logano has fared much better on the second-tier Nationwide Series. He has 13 career Nationwide wins, four this season, including last week at Dover International Speedway.
Martin is all too familiar with his runner-up spot at Pocono. He has yet to win in 51 career Cup races at Pocono and has finished second seven times.
Logano led a career-high 48 laps to become the youngest winner at Pocono. It was his second win in 125 career starts.
Matt Kenseth finished seventh and wrested the points lead away from Greg Biffle. Dale Earnhardt Jr. had the dominant car most of the race and finished seventh. Paul Menard and Jamie McMurray rounded out the top 10.
The first repave at Pocono since 1995 produced record speeds in qualifying -- 36 cars bettered the previous track record. And they flew on Sunday -- just a little too fast on pit road. Drivers were hit with a record Cup number of speeding violations entering or exiting pit road.
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