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.
"It's just exciting to see some explosive plays out there," Orgeron said. "That's part of our football team. That's what makes us who we are at USC. We have some great athletes on this team who can score at any time."
The Trojans haven't lost in this series since a triple-overtime defeat in Berkeley in 2003, outscoring the Bears by an average of 20 points in that span and not trailing at any point in a game since 2007.
The Bears went winless in six home games against FBS opponents this season. The 14-game skid against FBS teams is the longest active one in the country, and many of those games haven't even been close. Cal has been outscored by an average of more than 25 points per game in that skid.
"It's been hard," senior receiver Jackson Bouza said. "There's nothing easy about it because we feel like we're so much better than our record shows."