South Florida (5-4, 3-2 American Athletic Conference) trailed 17-15 before Flowers and Adams connected with 4:40 left in the game to cap a three-play, 85-yard drive.
East Carolina (4-5, 2-3) had two possessions with a chance to go back in front but gained only 19 yards over its final 11 plays.
Flowers threw for 200 yards and two TDs while running for another 79 yards. Marlon Mack ran 27 times for 117 yards and Adams caught four passes for 95 yards.
The Pirates managed just 29 yards on 18 plays in the first half but trailed only 12-7 at the break. They took the lead at 14-12 on James Summers' 3-yard TD run with 5:08 left in the third quarter.