Redd's 11-yard TD run put the Trojans ahead 10-0 and USC (5-1, 3-1 Pac-12) was never headed in its third straight victory.
Matt Barkley went 10-of-20 through the air for 167 yards and a score, and Anthony Brown returned a blocked punt for a touchdown for the winners.
Washington's Keith Price was plagued by two interceptions and two lost fumbles as the Huskies (3-3, 1-2) dropped their second consecutive game.
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