Tech shot 46.3 percent (25-54) from the field and UH shot 37.1 percent (23-62).
"We knew it was going to be a fight and I'm proud of the guys for executing," Tech head coach Kerry Rupp said.
Rolle was 11-of-18 from the field as he recorded his ninth double-double of the season. His 17 rebounds, nine offensive, was a career high.
Senior Kyle Gibson had 19 points, five rebounds and seven assists. Senior Jamel Guyton had a career-high 10 rebounds to go with his 14 points for his first-ever double-double game.
After a Guyton three-pointer rimmed-out, Rolle grabbed the offensive rebound in mid-air and slammed it for two points. On their next possession, Rolle hit a lay-up as he scored 13 of the Bulldog's final 18 points of the first half. At halftime Tech led 31-30.
The second half was very physical with bodies constantly hitting the floor. That fueled a 13-5 run to give LA Tech a 54-45 lead with 6:49 remaining capped off by a Guyton steal and dunk. That was the largest lead of the night for the Bulldogs.
With Gibson missing three-consecutive free throws in the final minute and UH converting back-to-back buckets, Tech's lead was down to just two, 61-59 with 33 seconds remaining. However, Gibson hit his next four free throws to preserve the lead and the five-point win.
The win breaks a three-game losing streak for the Bulldogs at UH.
Louisiana Tech will have a week to prepare for New Mexico State who comes to the Thomas Assembly Center on Saturday at 8 p.m. CT.