Torres struck for his tenth goal of the season in the 35th minute and the Goats held on to the precious three points to snap a four-match winless run and earn their first victory since May 11 against Colorado.
Real Salt Lake went down to 10 men inside the opening 10 minutes of play and never recovered, suffering their second consecutive defeat to extend their winless run to five games.
Things went south for RSL from the outset after young midfielder Luke Mulholland was shown a straight red card by referee Kevin Stott for a straight-legged, studs up tackle on Martin Rivero.
The goal came 10 minutes before the intermission as Tony Lochhead picked up his head on the left flank and whipped an inch-perfect cross into the area.
Torres tracked the ball perfectly and struck it beautifully on the volley straight into the top right corner, leaving RSL goalkeeper Jeff Attinella with no chance.
Playing down a man, RSL could never create any offensive rhythm, finishing the 90 minutes with only a single shot on target and a second straight defeat.
The result sees Chivas USA improve to 14 points on the season, while RSL remains in second place in the West with 25 points, 10 behind league leaders Seattle Sounders FC.