Davis hauled down the go-ahead score in the fourth quarter for the Longhorns (7-2, 4-2 Big 12), who notched their third straight win.
David Ash fired three scoring strikes in all, completing 11-of-19 passes for 264 yards for Texas.
Johnathan Gray led the Longhorns' ground game, compiling 106 yards on 20 carries.
The Red Raiders (6-3, 3-3), meanwhile, fell for a second straight time even though Seth Doege went 26-for-44 through the air for 329 yards and a touchdown.
Texas Tech got eight catches for 126 yards from Eric Ward.
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Couple mistakenly served bag of cash at McDonald's drive-thru