The Cougars trailed 21-10 in the first half, but held Tech's high-powered offense to one second half score.
Houston was playing as a ranked team for the first time in 18 years after knocking off then No. 5 Oklahoma State two weeks ago. A record crowd of 32,114, including Phi Slama Jama stars Hakeem Olajuwon Clyde Drexler showed up to cheer them on.
Less than a month into the season, the Cougars (3-0) from Conference USA have a couple of impressive wins against Big 12 teams to bolster their chances of breaking into the BCS.
Keenum kept the game-winning, 95-yard drive going with a 7-yard pass to Patrick Edwards on fourth-and-3.
The Red Raiders (2-2) led 28-23 midway through the fourth quarter before Will Ford's interception stopped a Cougar drive. But Tech couldn't convert and had to punt back to Houston with about six minutes remaining.
Tech had a last chance for the win but Taylor Potts' desperation throw on the last play of the game was broken up by the Cougars, sending thousands of Houston fans onto the field.
Keenum was 38 of 58 for 435 yards and had a touchdown pass and an interception in the first meeting between these two teams since 1995 when both were in the Southwest Conference.
It was the shootout most expected with the two teams combining for 1,063 yards of offense.
But the pass-happy Red Raiders relied more heavily than normal on their running game. Tech had gained 86 yards rushing in its first three games but had 163 Saturday.
Of course the Red Raiders still passed plenty, with Potts finishing with 321 yards and Tech's only second half score.
A hands to the face penalty by Tyrell Graham erased an interception with less than a minute left in the third quarter. But the Red Raiders weren't able to take advantage of the blunder and came away empty after Potts was stuffed for no gain on fourth down from the 1.
David Hunter forced his second fumble of the night when he made Tech freshman Eric Stephens cough it up late in the third quarter. C.J. Cavness recovered it for the Cougars.
They drove to the 4, but came away with only a field goal after three consecutive incomplete passes. That left the Red Raiders ahead 28-23.
Potts connected on a 24-yard TD with Tramain Swindall with about four minutes left in the third quarter. Swindall shed three Houston defenders, the last near the goal line, on the score that stretched Tech's lead to 28-20.
Bryce Beall's 1-yard run got Houston within 21-20 midway through the third quarter. A nifty 45-yard reception by Tyron Carrier got the Cougars in scoring position.
Harrison Jeffers pushed Tech's lead to 21-10 with a 13-yard run less than a minute before halftime. It was Tech's third rushing TD of the half after scoring three on the ground in the previous three games combined.
Mannisto hit a career-long 50-yard field goal at the end of the second quarter to make it 21-13 at halftime.
The Red Raiders relied on the run on a 69-yard drive capped by an 11-yard run by Baron Batch to take a 14-10 lead in the second quarter.
Keenum put the Cougars up early with a 6-yard touchdown pass to James Cleveland in the first quarter. It was his school-record 19th straight game with a touchdown throw, surpassing Heisman Trophy winner Andre Ware.
A 6-yard run by Batch evened it up at 7-all later in the first quarter.