Leading only 26-23 late in the third quarter, Bridgeport reeled off the final 24 points of the game to claim the victory.
Bulls quarterback Cody Henson was 19 of 33 passing for 290 yards on the night. His favorite target was Jordan Daniel, who had 110 yards receiving.
Bridgeport totaled 484 yards of offense while holding Burkburnett to just 200 yards, all on the ground, for the night.
The win improved Bridgeport's overall record to 2-4, but more importantly, it gives them a 1-0 start in district play. The Bulls will look to make it two in a row Friday when they host Iowa Park.