Bowyer pulled away from Burton following the final restart after the Richard Childress teammates had acted as a tandem during the majority of the 500-mile race.
Bowyer finished 0.018 seconds ahead of Burton, claiming his first win of the season and the fifth of his Sprint Cup Series career.
Neither qualified for this year's Chase for the Sprint Cup championship, while Burton was trying to snap a three-year series winless streak.
Carl Edwards' 11th-place finish boosted his lead over Matt Kenseth in the championship race to 14 points.
Celebrity Couples of 2014 [PHOTOS]