Harrison, who finished with 23 points and five assists, hit two layups, a free throw and a 3-pointer and Tulsa led 74-69 with 31 seconds left in overtime. Kendren Johnson hit a 3-pointer to pull Memphis within 74-72, but teammate Nick King's 3-pointer missed with four seconds left.
Trailing 36-34 at halftime, Tulsa led early in the second half, fell behind, then led 66-64 after Ray hit a 3 with 58 seconds left. The Tigers' Trahson Burrell tied it at 66 with a layup to send the game into overtime.
Shaq Goodwin led Memphis (17-12, 9-7) with 17, Johnson had 13 with five assists and Burrell scored 12.