Torres' one-touch finish to the upper near post, off a long cross by Tony Lochhead, came in the 35th minute. Lochhead stole the ball near midfield, took two dribbles, lobbed a pass to the inside of the penalty area and Torres timed it perfectly to put it past goalkeeper Cole Grossman.
Chivas USA (3-7-5) ended a four-game winless streak and recorded its first shutout of the season.
Real Salt Lake's Luke Mulholland was given a red card in the ninth minute for a studs-up tackle of Martin Rivero.
Salt Lake (6-3-7) was already without central midfielder Kyle Beckerman and goalkeeper Nick Rimando, who are playing in the World Cup for the U.S. The loss extended Real Salt Lake's winless streak to five matches.