Tulsa was held to a 31-yard Carl Salazar field goal to open the third extra period and Terrance Franks scored from 4 yards to give the Bobcats the win.
Tulsa (1-3) rallied from a 14-point deficit in the fourth quarter. Dane Evans threw a 17-yard touchdown pass to Conner Floyd to start the fourth quarter, then capped a 17-play, 75-yard drive by scoring from the 1 with 10 seconds left in regulation.
The teams traded touchdowns in the first two overtime periods.
Tyler Jones was 21 of 31 for 228 yards and two touchdowns passing and carried 20 times for 51 yards and a touchdown for Texas State (2-2).
Evans was 23 of 40 for 234 yards and two scores for Tulsa.