Daniel Spencer caught seven passes for 100 yards and a touchdown, while Greg Ward, Jr., had five receptions for 48 yards and a touchdown. Ryan Jackson rushed seven times for 62 yards and a touchdown, and Kent Brooks added a touchdown run for the Cougars, who totaled 365 yards.
Houston forced four turnovers - three interceptions and a fumble - and also had five sacks. Zach McMillan had two interceptions.
Houston (8-4, 5-3 American) earned its first shutout since 2011 and its first conference shutout since a 64-0 win over Rice in 1989.
Neal Burcham, who started in place of Garrett Gilbert - out with a left knee sprain - finished 27 of 52 for 212 yards and threw 3 interceptions for SMU (5-6, 4-3).
Jeremy Johnson had 8 receptions for 75 yards, and Darius Joseph caught 9 passes for 52 yards, while Prescott Line rushed 17 times for 81 yards for SMU, which finished 3 of 7 on fourth downs and gained 295 yards.
The Mustangs, who entered the game averaging almost 31 points, were held to scoreless for the first time since 2004 when they were shut out 42-0 at Fresno State.
O'Korn found Spencer on Houston's first offensive play for a 67-yard touchdown pass with 13:32 left in the first quarter to open up a 7-0 lead.
After Burcham was intercepted by Adrian McDonald to give the Cougars possession at SMU's 29, Kyle Bullard upped the lead to 10-0 with a 27-yard field goal with 5:23 left in the first. Bullard added a 27-yard field goal with 2:48 left in the third.
O'Korn found Ward for a 19-yard touchdown grab two minutes into the second quarter to up the lead to 17-0.
Brooks extended Houston's lead to 24-0 with a 1-yard touchdown run 34 seconds before halftime after Eric Eiland set the Cougars up with a 62-yard fumble return off a bad snap down to the SMU 1 before being tackled by SMU's Kevin Pope.
Jackson added a 33-yard touchdown run with 8:07 left in the third to give the Cougars a 31-0 lead.
SMU struggled moving the ball in the first half, gaining 53 yards and two first downs in the first quarter and 146 yards in the first half to go along with three turnovers and 9 penalties for 75 yards.
Both times SMU got inside the Cougars' 35 in the first half resulted in turnovers - the first a McMillan interception in the end zone when SMU reached the Houston 22 and the second was Eiland's fumble recovery when the Mustangs were at the Houston 32.
SMU got in the red zone with five minutes left in the fourth, but Line was stopped a yard short of the first down on fourth and 6 from the Houston 15.