After Josh Davis converted a three-point play for Tulane to tie it 91-91, Young made two free throws with 54 seconds left to put Houston on top 93-91.
Davis responded with a layup and Kendall Timmons made 1 of 2 from the foul line with 12 seconds remaining to put the Green Wave ahead 94-93.
Young, with 2 seconds left, connected on a jumper while getting fouled. Young made the and-1 free throw to put Houston on top for good 96-94.
Kendall Timmons led Tulane (18-13, 6-10) with 22 points and eight boards. The Green Wave has lost four straight.