Farrow scored the go-ahead TD on a 2-yard run at 3:06 in the fourth quarter to give Houston (6-4, 4-2 American Athletic Conference) a 35-28 lead.
Greg Ward Jr. was 17 of 22 for 225 yards passing, including a 17-yard TD pass to Keyarris Garrett to tie it at 21 in the third quarter.
Dane Evans passed for 258 yards and two TDs for Tulsa (2-9, 2-4), including a 1-yarder to Zach Epps to tie it at 28 early in the fourth quarter. Evans also ran for a score and Zack Langer scored on a 2-yard run.
Farrow scored two TDs on 1-yard runs, then cracked a 45-yard scoring run to put Houston up 21-14 in the third quarter.
Adrian McDonald intercepted a pass by Evans on the ensuing drive, and Kyle Bullard kicked a 35-yard field goal four plays later.