Shaq Goodwin added 17 points and Ricky Tarrant Jr. 16 for the Tigers (9-3), who have won 12 straight league openers dating back to their days in Conference USA.
Malik Martin had 18 points and Cameron Reynolds had 13 of his career-high 15 in the first half for the Green Wave (7-7), who led 37-35 at the break. Dylan Osetkowski had 15 points and 10 rebounds.
Tarrant, a senior who played his first two seasons at Tulane, had 12 points in the second half, including seven straight that put the Tigers up 42-41 with 16:39 to play.
Tulane regained the lead on a Louis Dabney 3 but after tying the game at 46 the Green Wave went scoreless for 3 1/2 and the Tigers pulled way.