Webb completed 28-of-41 passes for 403 yards, hooking up twice with Jakeem Grant and once each with Bradley Marquez and Rodney Hall as the Red Raiders (8-5) built up a 27-13 halftime advantage.
Reginald Davis returned a kickoff 90 yards for a score to turn back a Sun Devils rally in the third quarter and secure a victory as Texas Tech broke a five-game losing streak ending the regular season.
Taylor Kelly supplied 260 yards of total offense for ASU (10-4), which fell to 0-4 in the Holiday Bowl.
Kelly ran for 135 yards with a score on 25 carries while D.J. Foster added 131 rushing yards and a TD on 20 tries.