Syracuse (2-6, 1-3) used big scoring plays from receiver Da'Mon Merkerson and freshman tailback Antwon Bailey to win just its third Big East Conference game under embattled coach Greg Robinson, now 3-22 overall in four seasons against conference foes.
Merkerson caught a 38-yard touchdown pass in the second quarter to give Syracuse a 14-7 lead at halftime. Bailey made it 21-7 in the third period when he shook off several tacklers on a 39-yard scoring run, his first collegiate touchdown.
Syracuse finished its scoring with an 8-yard touchdown toss from Cam Dantley to fullback Tony Fiammetta with 5:16 to play.
Brinkley finished with a career-high 166 yards on 33 carries, breaking a record he shared with Joe Morrison and James Mungro.
Louisville (5-3, 1-2) was riding a three-game winning streak and was coming off a 24-20 upset win over then-No. 14 South Florida.
Troy Pascley caught a 37-yard touchdown pass with 3:55 remaining to pull the Cardinals within a touchdown at 28-21.
The Orange was a 37-point underdog last season when it shocked Louisville 38-35 at home, ending the Cardinals' 20-game home winning streak.