Woods, a sophomore, entered the game with 99 catches, three shy of Keyshawn Johnson's record set in 1995. Woods equaled the record late in the first quarter and broke it on the first play of the second. He finished the game with 12 receptions, giving him 111 this season.
Freshman receiver Marqise Lee caught 13 passes for 225 yards and two touchdowns.
When Woods pulled in his 10th catch of the game, a six-yard gain, on USC's second drive of third quarter, it made history. No two USC receivers before had received double figures in receptions in the same game.
Lee finished with 73 catches for 1,144 yards receiving this season. Woods had 1,292 receiving yards, giving the Trojans two 1,000-yard receivers for the fourth time.
Mike Williams and Keary Colbert achieved the feat in 2002 and 2003. Steve Smith and Dwayne Jarrett did it in 2006.
Junior running back Curtis McNeal rushed for 124 yards, including a 73-yard touchdown. McNeal finished with 1,005 yards this season.
Matt Barkley had an almost-perfect first quarter against UCLA. The junior quarterback completed 16 of 17 passes for 168 yards and two touchdowns in the first 15 minutes. Lee had eight first-quarter catches for 100 yards, and Woods had six receptions for 38 yards.
Trojans running backs were also fast out of the gate. McNeal and Marc Tyler averaged 20.8 yards in five carries.
Junior safety T.J. McDonald got his team-leading third interception in the second quarter.
It's been a tough season for McDonald, who intercepted two passes against Arizona on Oct. 1.
McDonald, the son of former USC All-American Tim McDonald and the brother of UCLA cornerback Tevin McDonald, was suspended by the Pac-12 Conference for the first half of USC's game against Colorado after making what was deemed an illegal hit on Stanford receiver Chris Owusu.
McDonald, who is weighing whether to enter the NFL draft or return for a final season of eligibility, came up big against the Bruins.
USC led 29-0 late in the first half when the Bruins looked as if they might rally for a late score.
The Bruins drove to USC's seven-yard line, but defensive end Nick Perry pressured UCLA quarterback Kevin Prince on third down, and McDonald intercepted a pass in the end zone, ending the threat and returning it more than 20 yards.
Fifth-year seniors Chris Galippo, Christian Tupou and DaJohn Harris were among the two dozen seniors who were introduced before the game.
The players were shown on the video board, ran through the tunnel to meet Coach Lane Kiffin and then continued onto the field and met family members.
Times staff writer Mike Hiserman contributed to this report.