Tevon Saddler scored eight of the Colonels’ last 10 points of the first half to send Nicholls to halftime with a 45-28 lead. Saddler hit a 3 with 17:39 left for 50-30 lead before Nicholls went cold and shot 6 of 29 from the field the rest of the way.
Cornish overcame nine turnovers and scored 13 points in the last 12 minutes. His layup with 5:18 to go put Tulane (8-3) up 60-59 and the Green Wave never trailed again.
Melvin Frazier and Ray Ona Embo each scored 12 for Tulane now 6-0 at home.
Saddler led the Colonels with 24 points and nine rebounds and Jahvaughn Powell had a career-high eight steals. Nicholls (5-6) finished with a total of 15 steals. Kimani Jackson added 16 points for Nicholls.