Salt Lake were dominating the game and were denied the lead by the woodwork when Khari Stephenson's low free kick beat the wall and Rowe but smacked off the post and was cleared.
The home side took the lead just before half time when Robbie Findley found Stephenson on the edge of the area and his low shot went under Rowe and into the net.
However, Salt Lake were pegged back immediately as Galaxy drew level through Landon Donovan when he volleyed the ball past Rimando with a lovely finish into the top corner.
After the break, both sides pushed for the lead but it was the hosts who finally got the goal when Garcia headed Morales's cross pas Rowe into the bottom corner.
Garcia made sure of the three points in added time as he slotted the ball past Rowe with a low finish from Morales's through-ball.