The Indiana-born racer defied the odds by stretching his fuel mileage long enough while remaining in control once he overtook Richard Childress Racing's Clint Bowyer for the lead following the penultimate restart.
Given the way the last few cautions fell and with track position being crucial, most of the top runners had to save fuel in their last stint, some managing to just make it to the end while others could not.
Penske's Kurt Busch was running second to Newman in the final stint but ran out on the final lap, finishing 10th, while Tony Stewart, who had pitted for the last time later than his team-mate, was able to attack in the last few laps on his way to second place ahead of Denny Hamlin.
The Stewart-Haas pair had swept the front row of the grid in qualifying and finished in the exact same order after the 301 laps scheduled following the fuel-saving drama. Their feat marks the first time a team has swept the front row and the top two spots in the race since Darrell Waltrip and Ken Schrader did so in the 1989 Daytona 500 for Hendrick Motorsports.
"I knew I was doing a really good job of saving fuel, which is not the easiest thing to do," said Newman, who got a perfect score by leading the most laps. "Here is easier than other racetracks, but still not easy to do. Saving grace that we had was we had a good racecar, we were able to pull out on a lead and maintain that lead."
Newman's win moved him up a spot in the standings to eighth place, but his victory gives him a mulligan that places him solidly in contention for a Chase berth in eight weeks' time.
Stewart's second place did not help him much in the standings as he is still in 11th, but the two-time Cup champion was still very pleased with his outfit's performance, which was arguably its best ever.
"It was a perfect day for the organisation for sure," said Stewart. "This is a perfect way to go into an off weekend, for sure. Especially going into Indy, man, this is big for everybody at Stewart-Haas Racing."
Hamlin overcame a spin following contact with AJ Allmendinger almost halfway through to race his way up to third in the end, succeeding with fuel saving tactics which had not been his team's strong suit recently.
His Joe Gibbs Racing team-mate Joey Logano was fourth, ahead of a charging Jimmie Johnson, who was sixth following a spin while battling for position with Earnhardt Ganassi's Juan Pablo Montoya 72 laps from the end.
Johnson's Hendrick Motorsports team-mate Jeff Gordon looked to be the car to beat but ran into electrical issues that put him a lap down. Impressively he made it back up to third but while running fourth shortly before the chequered flag his car's right-front tyre blew up, forcing him to coast to the end.
"With the alternator issue, which caused me to have to turn my A/C off and brake blowers, which probably ultimately blew that right front tyre there at the end," said Gordon, who finished 11th. "It was a challenging day in a lot of ways. But it was certainly something."
Former points leader Kyle Busch had a similar tyre-related issue which sent him against the wall and to the garage area for lengthy repairs. Carl Edwards was 13th and regained the points lead while Kurt Busch and Johnson moved up to second and third respectively ahead of Kevin Harvick, who had a lacklustre run to 21st.
Results - 301 laps: Pos Driver Team/Car Time/Gap 1. Ryan Newman Stewart Haas Chevrolet 3h03m33.000s 2. Tony Stewart Stewart Haas Chevrolet + 0.773s 3. Denny Hamlin Gibbs Toyota + 3.488s 4. Joey Logano Gibbs Toyota + 8.125s 5. Jimmie Johnson Hendrick Chevrolet + 8.481s 6. Kasey Kahne Red Bull Toyota + 8.504s 7. Bobby Labonte JTG Daugherty Toyota + 12.211s 8. Martin Truex Jr Waltrip Toyota + 12.486s 9. Marcos Ambrose Petty Ford + 12.731s 10. Kurt Busch Penske Dodge + 13.082s 11. Jeff Gordon Hendrick Chevrolet + 14.325s 12. AJ Allmendinger Petty Ford + 16.529s 13. Carl Edwards Roush Fenway Ford + 16.844s 14. David Ragan Roush Fenway Ford + 17.943s 15. Dale Earnhardt Jr Hendrick Chevrolet + 18.960s 16. Jeff Burton Childress Chevrolet + 21.169s 17. Clint Bowyer Childress Chevrolet + 21.572s 18. Greg Biffle Roush Fenway Ford + 21.871s 19. David Reutimann Waltrip Toyota + 22.044s 20. Matt Kenseth Roush Fenway Ford + 22.302s 21. Kevin Harvick Childress Chevrolet + 22.506s 22. Mark Martin Hendrick Chevrolet + 22.848s 23. JJ Yeley Front Row Ford + 25.965s 24. Paul Menard Childress Chevrolet + 26.420s 25. David Gilliland Front Row Ford + 26.916s 26. Landon Cassill Phoenix Chevrolet + 1 lap 27. Scott Wimmer Gordon Dodge + 1 lap 28. Andy Lally TRG Chevrolet + 1 lap 29. Dave Blaney Baldwin Chevrolet + 1 lap 30. Juan Pablo Montoya Earnhardt Ganassi Chevrolet + 1 lap 31. Jamie McMurray Earnhardt Ganassi Chevrolet + 1 lap 32. Mike Bliss FAS Lane Ford + 2 laps 33. Regan Smith Furniture Row Chevrolet + 3 laps 34. Brian Vickers Red Bull Toyota + 18 laps 35. Brad Keselowski Penske Dodge + 44 laps 36. Kyle Busch Gibbs Toyota + 77 laps Retirements: David Stremme Inception Chevrolet 159 laps Casey Mears Germain Toyota 83 laps Erik Darnell Whitney Chevrolet 72 laps Michael McDowell HP Toyota 46 laps Joe Nemechek NEMCO Toyota 37 laps Mike Skinner Germain Toyota 17 laps Jeff Green Front Row Ford 11 laps