Chivas nearly went ahead in the 20th minute when Donny Toia drilled an effort at goal from the edge of the area, but his shot clipped the post and went wide.
Joao Plata could have given the 10 men the advantage when he managed to get behind the Chivas defence, but when under pressure he could only fire his effort wide of the post.
Salt Lake were punished for this missed chance when the home side took the lead in the 34th minute in spectacular fashion as Torres caught Tony Lochhead's cross first time on the volley and his effort raced past Jeff Attinella into the top corner.
After the break, Mauro Rosales should have doubled his side's lead when he controlled the ball into the box and let fly with a shot on the half-volley, but his effort went just over the bar.
Chivas continued to search for the second goal to kill off the game and nearly found it when Carlos Alvarez won the ball in the box, although his low shot went inches wide of the post.
Real made a last-ditch attempt to try to salvage a point from the game but were unable to beat Dan Kennedy as the home side secured the three points.