Agholor scored on returns of 75 and 93 yards to tie the record set by Mike Garrett against California in 1965.
Agholor's 168 yards in returns broke the record of 162 set by Garrett.
Josh Shaw also scored on a blocked punt as USC tied the NCAA record for most punts returned for touchdowns in game.
The returns helped USC extend its win streak against Cal to 10 games. The Trojans' 62 points were the most since scoring 56 against San Jose State in 2009.
Agholor's return for a touchdown was USC's first since Anthony Brown returned a blocked punt last season against Washington.
It was the first unblocked punt return for a touchdown since Ronald Johnson scored on an 89-yard return against Hawaii in 2010.
Quarterback Cody Kessler completed 14 of 17 passes for 170 yards and two touchdowns.
Because USC was so far ahead, backup Max Wittek attempted a pass for the first time since playing against Boston College on Sept. 14.
Wittek completed three of four passes for 73 yards, including a 44-yard completion to receiver De'Von Flournoy.
Senior tailback Silas Redd scored a touchdown late in the first quarter on a screen pass, but he was removed from the game because of a right knee injury suffered a few plays before.
Redd was hurt on a running play after he hurdled one defender and was hit by two others.
After the game, Redd said he was fine.
Defensive lineman Leonard Williams did not play because of a shoulder injury suffered against Oregon State.
Kevin Graf, who sat out against Oregon State because of an ankle injury, started at right tackle.
Isaac steps up
Freshman tailback Ty Isaac rushed for 87 yards in 11 carries and scored his first career touchdowns in the second half.
Isaac's four-yard run in the third quarter put USC ahead, 55-14.
"I was thinking, 'No one is going to stop me. I've got to get in,' " he said.
Isaac ran for a 37-yard touchdown early in the fourth quarter for a 62-21 lead.
"I was just trying to get a first down, to be honest with you," he said. "And then it kind of opened up and I was like, 'Man, I'm going to go get it.' "
This has been a tough first year for Sonny Dykes at Cal, as his team fell to 1-9 on his 44th birthday.
The Bears played tough in an early loss to Northwestern but have since been decimated by injuries.
"A lot of these young guys have been forced to play because there is nobody else," Dykes said. "It's OK. It has been tough this year, but it is going to pay off…. In a weird sort of way, the experience they have gotten this year and the hard luck will help our team respond faster.
"We are going to get this thing right. I don't have any doubt in my mind. I feel more strongly about that right now than I did Dec. 5 when I was hired."
Redshirt freshman linebacker Jabari Ruffin had a team-best nine tackles for the Trojans…. Third-year sophomore lineman Charles Burks recorded his first sack.