The two players now hold the school's all-time single-game and career records for touchdown passes and receptions.
Barkley's second-quarter scoring pass to Woods was the 100th of his USC career, breaking Matt Leinart's seven-year-old mark of 99. Barkley tied Leinart's record in the first quarter with an 8-yard touchdown throw to Xavier Grimble.
Barkley exited the game with 10 minutes remaining in the third quarter of an eventual 50-6 win. In two career games against the Buffaloes, Barkley has 12 touchdown passes with only one interception.
Woods entered Saturday's game with 212 receptions, four behind Dwayne Jarrett's all-time mark. He caught his first ball on USC's first play from scrimmage, added a 39-yard touchdown catch on the Trojans' next drive and grabbed one pass on the next three drives, setting the record on a 29-yard catch near the end of the first half.
Woods also set a school record for touchdown catches in a game with his fourth scoring grab in the third quarter.
USC showed a previously produced video at the L.A. Memorial Coliseum commemorating Barkley's achievement shortly after he set the record.
Chris Paul and Blake Griffin of the Los Angeles Clippers congratulated him on the video, as well as Landon Donovan of the L.A. Galaxy. Leinart and Carson Palmer filmed a spot at Raiders practice in Oakland, and Keyshawn Johnson also had a quick clip
Former Trojans coach Pete Carroll drew the loudest applause from the sold-out Coliseum crowd. USC showed a similar video when Woods broke his record a few minutes later.
Barkley finished the day 19 of 20 for 298 yards and six touchdowns, with the touchdown total matching a school record he set last season against the Buffaloes. His only incompletion came on a dropped pass by McNeal.
Barkley's 95 percent completion rate also broke the Pac-12 record by former UCLA quarterback Rick Neuheisel.
Woods exited with eight catches for 132 yards and four touchdowns.