The Cougars (8-1, 4-1 Conference USA) rushed onto the field and hoisted Hogan into the air after he connected on the longest kick of his career. He hadn't made a field goal of longer than 34 yards before his game-winner.
Tulsa players splayed out on the field after the deflating loss.
Keenum finished with 522 yards on 40 for 60 passing with three touchdown passes. It was the second straight game with more than 500 yards passing for the nation's most prolific passer.
Only a few minutes earlier, Keenum was walking off the field with his hands on his helmet.
But Tim Monroe recovered the onside kick for Houston, and Keenum connected on a 14-yard pass to James Cleveland and a 13-yarder to Tyron Carrier to set up Hogan's kick with 3 seconds left. He drilled the ball just inside the left upright, igniting the Cougars' celebration.
Charles Clay ran for two scores and also caught two touchdown passes, and G.J. Kinne threw for a career-best 334 yards and three touchdowns for Tulsa (4-5, 2-3). The Golden Hurricane had kept Houston out of the conference championship game the last two years as West Division champions.
The Cougars, slotted 15th in the BCS standings at the start of the day, stand to move up after losses by Oregon, Penn State and LSU. But only after more heroics from Keenum, who threw for a career-high 559 yards and five touchdowns -- including the game-winner with 21 seconds left, coincidentally, last week against Southern Miss.
The Golden Hurricane had kept the Cougars at bay in the fourth quarter, getting a goal-line stand and then forcing Keenum & Co. to settle for a field goal on their first two drives.
Keenum handed off four straight times after reaching first-and-goal at the 10 with a chance to take the lead. Tanner Antle and Dexter McCoil stood up Bryce Beall on fourth-and-goal from the 1 to get the ball back, but Houston got the ball right back after a three-and-out.
Keenum found Cleveland for a 19-yard pickup on third-and-20 on the next drive, and Sumlin settled for Hogan's 26-yard field goal to get within 38-37 with 8:08 to play.
Clay jumped into the end zone from 1 yard out to put the Golden Hurricane ahead by eight in the final 3 1/2 minutes, but that only set the stage for Keenum and Hogan.