Case Keenum completed an impressive 35-of-40 passes for 318 yards, which gives him 1,426 career completions and broke the NCAA record 1,403 yards held by Graham Harrell of Texas Tech.
Keenum also ensured his third 4,000-yard season and 36th 300-yard game, which tied the records in those categories set by Hawaii's Timmy Chang.
Keenum hit Justin Johnson for a 12-yard touchdown and ran in a 16-yard score in the fourth quarter to give Houston (11-0, 7-0 Conference USA) a 30-7 lead.
J.J. McDermott was 23-for-40 passing for 239 yards and a touchdown for SMU (6-5, 4-3). The Mustangs lost their fourth game in their last five tries. They were outgained by the Cougars in total yardage 513-263.