Tied at 32 at the half, the Owls moved ahead on Seth Gearhart’s three-point play before the Green Wave (14-6, 2-3) took control with a 9-0 spurt.
After Julian DeBose’s layup got Rice back within four, at 41-37, Ricky Tarrant made two free throws and Tulane maintained a cushion of at least six points from there.
The win gave the Green Wave a 25-24 lead in the series and snapped Rice’s three-game streak, including a sweep last season.
Davis had nine rebounds, ending his run of three straight double-doubles, as Tulane outrebounded the Owls 38-21.
Tarrant added 16 points and Jordan Callahan scored 10 for the Green Wave.
Gearhart scored 23 points to lead the Owls (4-15, 0-5), who have lost eight of their past nine games.