Stark made three of the Green Waves five 3-pointers and Dabney added nine rebounds.
The score was tied at 27 at the break, but Tulane (9-8, 1-1) opened up the second half with a 9-0 run. The Mean Green climbed within four (54-50) with 9:02 remaining on the clock, but Tulane quickly shut down any hope of a comeback with a 12-3 run to go up 66-53 with 4:11 left to play.
T.J. Taylor came off the bench to lead with 19 points on 5-of-10 shooting and finished with four of the Mean Greens five assists.
North Texas (9-7, 0-2) has yet to pick up a conference win in its first year as a member of the Conference USA.