Riley Nelson threw three touchdown passes to yarder with 11 seconds remaining in the fourth 21, in the Armed Forces Bowl.
Nelson completed 17-of-40 passes for 250 yards with two interceptions for the Cougars (10-3), who made their seventh consecutive bowl appearance under head coach Bronco Mendenhall.
Hoffman finished with 122 yards on eight receptions.
Tulsa's G.J. Kinne matched Nelson with three touchdown passes, but the Golden Hurricane (8-5) couldn't get BYU's offense off the field down the stretch.