Bruce Lahay kicked fourth-quarter field goals of 46 and 21 yards to win it in Fayetteville, Ark.
With Arkansas trailing, 10-8, with nine minutes to play, quarterback Tom Jones directed the Razorbacks from their 31 on a drive that took them to the Tulsa 28 before Lahay kicked what turned out to be the winning points.
Lahay, whose punting kept Arkansas in a hole much of the day, added a 21-yard field goal moments later when Tulsa's fourth-down fake punt failed at its own 11.
Arkansas is 1-0 and Tulsa is 0-2.
Jason Staurovsky's 42-yard field goal in the third quarter gave Tulsa a 10-0 lead.
Arkansas got back in the game on a wobbly pass by running back Thomas Brown. Wide receiver Derek Holloway caught the ball, spun away from one defender and turned the play into a 41-yard touchdown with 1:14 left in the third period.
Tulsa played conservatively while leading, throwing only one pass until Lahay's first field goal, and kept Arkansas backed up with the punting of Steve Cook. The Razorbacks kept themselves in trouble with kicking game mistakes.
Arkansas linebacker Steve Douglas sealed the victory on a pass interception with 45 seconds remaining.