Cobbs had been mired in a four-for-20 skid before going eight for 10 from the floor against the Trojans. The Golden Bears' point guard made his final five shots and added seven assists while helping Cal (18-9, 9-5 Pac-12) split the season series with its intra-state rival.
Ricky Kreklow had 12 points off the bench while Bird and Tyrone Wallace scored 10 points apiece for the Bears.
Pe'Shon Howard scored 17 points for the Trojans (10-17, 1-13), who have lost eight straight.
The game between two teams headed in opposite directions was much closer than anticipated until Bird helped Cal pull away.
He split past two USC defenders to score on a fastbreak, then made back-to-back threes to give the Bears a 72-60 lead.
After a basket by the Trojans' Strahinja Gavrilovic, Cobbs scored on a layup and made the free throw to complete the three-point play.
Cobbs made it through the game despite a pair of hard collisions with USC players. Both times, Cobbs lay prone on the court momentarily before getting up and hobbling off.
The Bears needed all they could from the senior guard, who needs three assists to move past Jason Kidd into fourth place on Cal's career list.
Coach Mike Montgomery's team shot just 36.7 and was limited to 27 points in the first half.
Wallace's quickness on the break, along with a lift from Kreklow, got Cal going. The duo, limited to a combined two-for-nine shooting in the first half, did all the scoring during an 11-0 run early in the second half.
Kreklow added three straight free throws to push Cal's lead to 64-56.
The Trojans were coming off another sluggish effort during Thursday's 80-59 loss at Stanford but didn't have much trouble keeping up with the inconsistent Bears.
Howard had 11 points in the first half, five coming as part of an 11-3 run by USC just before the break. Julian Jacobs added a three-pointer and Omar Oraby scored the final three points of the half to put the Trojans up, 30-27.