Jones also hit a career-long 51-yarder for a 10-7 lead in the first quarter and a 34-yarder with two seconds left in the first half for a 20-14 halftime edge.
Hellums carried 30 times for 121 yards and three touchdowns and went 7 for 12 passing for 64 yards. He opened the scoring with a 41-yard touchdown run on fourth-and-1 on Army's first possession. His 1-yard fourth-down score late in the second quarter capped a 15-play drive that took 9:51 off the clock. Godspower Nwawuihe ran 12 times for 135 yards, including a 66-yard touchdown on Army's second play of the third quarter. Zach Mundell's two-point run made it 28-14.
Tulsa answered quickly. David Wells Jr. scored on an 11-yard run, and Trequan Jones broke a 59-yard touchdown run to tie it at 28 going into the fourth quarter. Hayes went 23 for 34 for 262 yards with two touchdowns and an interception. Calloway caught 10 passes for 88 yards, and Javon Ross scored twice, once on the ground and once through the air.
Army ran for 275 yards on 51 carries, held the ball for 33:34 and did not turn it over. It went 3 for 4 on fourth down.
Army is 5-2 and 4-1 in the American Conference and plays at Memphis on Oct. 31. Tulsa falls to 4-4 and 1-3 and plays at Tulane on Nov. 7.