Turner’s go-ahead run was confirmed by review after it appeared he might have been down before crossing the goal line.
The Owls (4-6, 2-4 Conference USA) withstood a comeback led by Ryan Griffin, who threw for 476 yards and four touchdowns, including three in the second half when Tulane (2-7, 2-3) rallied from a 28-10 halftime deficit.
Rice led 14-0 early after two touchdown runs by Taylor McHargue. The second came after the Owls recovered a Tulane fumble on the kickoff following the first score.
Tulane gained all its offensive yardage by passing, netting 0 yards on 14 rushes.