Brennan completed 44 of a school-record 75 passes for 547 yards and four touchdowns, as the 16th-ranked Warriors improved to 7-0.
The Hawaii quarterback overcame four interceptions and rallied his team from a 14-point deficit in the final 3:35 of regulation. He tied it with 31 seconds remaining on a two-yard run.
The Warriors had the ball first in overtime and took four plays to go 25 yards for the score. After Brennan's touchdown pass, Hawaii's Myron Newberry intercepted a pass from Adam Tafralis in the end zone.
Brennan hit Ryan Grice-Mullen with a 16-yard scoring pass to give Hawaii a 14-7 halftime lead. San Jose State (3-4) got an interception return for a touchdown and two scoring passes from Tafralis to move in front in the second half.
Brennan hit C.J. Hawthorne with a 34- yard TD pass in the third period and then connected with Davone Bess on an 11-yard scoring strike that brought the Warriors within seven with 3:35 left in regulation.