Jones scored nine straight points to put the Cougars ahead 68-64.
Boogie Ellis got fouled and missed the first free throw. He missed a 3-pointer with 31 seconds remaining and finished with 18 points for the Trojans (8-8, 2-3). Isaiah Collier added 12 points.
Bronny James was the only Trojan not to score, going 0 for 3 in 15 minutes in front of his father, LeBron James. He sat down with 7 1/2 minutes left and didn't return until the final 29 seconds.
Over the final 8 minutes, the Cougars went 14 of 15 from the line while making just four field goals.
Harrison Hornery's 3-pointer gave USC its last lead, 64-63. It was also the Trojans' last basket as they failed to score over the final 2:16.
Neither team led by more than six points in the game until the Cougars score the last nine points of the game.