The Houston defense forced multiple turnovers for the 13th straight game and took the ball away four times in the game including three first-half takeaways.
Efrem Olipant led the Cougars in tackles for the second-straight week with 13 stops on the day and forced a fumble in the third quarter.
O'Korn finished 13 of 30 and Deontay Greenberry caught four passes for 76 yards for the Cougars (5-0, 2-0 American), who were out-gained 349 yards to 247.
Paxton Lynch was 21 of 41 for 222 yards passing, and Brandon Hayes rushed 12 times for 72 yards to lead the Tigers (1-4, 0-2), who committed four turnovers - all fumbles. Mose Frazier caught five passes for 81 yards.
Trailing 15-10 midway through the third, Farrow put the Cougars ahead with a 1-yard run and followed that by taking O'Korn's shovel pass in for a two-point conversion.
Farrow extended the lead to 25-15 with a 6-yard run with 10 minutes remaining. Fullback Luke Stice delivered a crushing block to spring Farrow into the endzone.
The touchdown gave Houston a score in every quarter this season and 27-straight quarters with points dating back to last season.
Jake Elliot had five field goals for Memphis. It was the first time since Houston's 56-3 win over East Carolina in 2011 the Houston defense held the opponent without a touchdown.