Callahan added four steals while Tarrant had five assists. Josh Davis had 11 points and eight rebounds for the Green Wave (7-2).
Freshman T.J. Carpenter notched a career-high 15 points for the Colonels (1-4).
Nicholls State was without Fred Hunter (hamstring strain) and Lachlan Prest (concussion) for the second straight game.
The win makes Tulane 4-0 on its current homestand, and the Green Wave has now won 19 of 20 all-time showdowns with Nicholls State.
Tulane led 23-12 with just under 8 minutes left in the first half, but the Colonels cut the lead to 30-24 by halftime.
Callahan hit a 3 then Davis made a dunk and two free throws to put Tulane up 37-24 after the break. Nicholls State never pulled closer than eight after that.