Trailing 34-7 near the end of the third quarter, Keenum found Patrick Edwards for a 50-yard touchdown to cut the lead to 34-14. Touchdown runs of 2 and 4 yards by Bryce Beall cut it to 34-28.
With less than two minutes remaining, Keenum connected with E.J. Smith for 26 yards, and then found Edwards again for a 32-yard scoring catch that put the Cougars (3-0) ahead to stay.
"It was a busted play actually," Keenum said of the game-winner to Edwards. "We never throw that pass. It was just a back-side post, and he just made one of the best catches that I have ever seen in my life."
The senior quarterback completed 25 of 40 passes for 351 yards and three touchdowns.
"We made it interesting, that is for sure," Keenum said after the game. "It was really the same story as last week for us. We had to put together some drives late in the game again. It's not ideal what we are doing right now but I'll take it."
Cougars' coach Kevin Sumlin credited his team's veteran leadership for the big win.
"We have guys who know what it takes to win," he said. "You look at who made those plays at the end of the game -- our senior class -- these guys who have been in a lot of big ball games, and they understand it and how to win."
After Keenum's 54-yard scoring pass to Michael Hayes in the second quarter brought Houston within 10-7, Louisiana Tech (1-2) scored the next 24 points, including two rushing touchdowns by Ray Holley.
