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Franklin scored six points down the stretch as the Aztecs (4-1) earned their fourth consecutive win since dropping their opener against Syracuse on the USS Midway. Rahon was 6 for 7 from the field, making all three of his 3-point attempts.
Xavier Thames scored 14 points and JJ O'Brien added 12 for San Diego State.
Eric Wise led USC (3-3) with 14 points, and Dewayne Dedmon grabbed 10 rebounds.
The Trojans opened the second half with an 18-4 run to take a 41-39 lead on a basket by Eric Wise with 13:28 to play. The game remained tight until San Diego State grabbed control at the end.
USC was assessed two technical fouls in the final two minutes. Thames and Jamaal Franklin made 5 of 6 free throws and Rahon had a clutch 3-pointer to extend the Aztecs' lead to 64-57 with 1:02 to play.
San Diego State has won 10 straight games against Pac-12 schools and 25 in a row against California teams over the past 3 years. The Aztecs also earned their first win in seven games at the Galen Center.
The Aztecs held USC to three baskets over the final 5:26 of the game.
San Diego State got off to a fast start. Thames' 3-pointer made it 12-2 with 14:36 to go in the first half.
The Trojans missed nine of their first 10 shots and committed four turnovers in the first 8 minutes.
Rahon nailed
Ari Stewart hit a 3-pointer down the stretch to help USC close to 35-23 at the break.
The Aztecs were without second-leading scorer Chase Tapley, who is sidelined with a strained patella tendon. He is expected to return next Saturday when San Diego State faces No. 11 UCLA.
The Aztecs have 23 of their last 28 road games.
