The latter two drivers dominated most of the race, but the Hendrick Motorsports teammates -- along with Clint Bowyer -- all made contact and spun around during the first two-lap overtime finish.
That enabled Newman, who had bumped Bowyer, to move into the lead. He then held off A.J. Allmendinger during the second and last green-white-checkered attempt, claiming his 16th career Sprint Cup Series win.
It was Newman's first victory since July at New Hampshire and denied the Hendrick team a milestone 200th Sprint Cup win.
Allmendinger finished second, 0.3 seconds behind, while Dale Earnhardt Jr. came in third.
Matt Kenseth and Martin Truex Jr. rounded out the Top 5.