Agholor started the scoring for USC (7-3, 4-2 Pac-12) with a 75-yard return and added a 93-yarder late in the second quarter to help USC win for the fourth time in five games under interim coach Ed Orgeron.
Josh Shaw also returned a blocked punt 14 yards for a score earlier in the second quarter for the Trojans, who tied the record last achieved by Oklahoma against UCLA in 2003 when Antonio Perkins returned three punts for scores.
"The best thing about getting that first return is it gave the rest of the guys confidence that they know they could block the same way," Agholor said. "They knew we were going to return another one. That's how I felt. We returned one and they were like, 'Let's do it again.' "
The Trojans had far too much speed for the Golden Bears (1-9, 0-7) to handle as Allen scored on runs of 43 and 79 yards and a 57-yard screen pass from Cody Kessler to extend USC's dominance over Cal.
Allen ran for 137 yards on six carries to go with his one long catch, giving him six touchdowns the past two weeks after struggling to get on the field early in the season.