Salt Lake picked up three road points in dramatic fashion when Kyle Beckerman fired a one-timer that Bobby Shuttleworth was able to stop. Garcia, however, was there to blast home the rebound and improve Salt Lake to 5-4-2.
New England opened the scoring on Ryan Guy's goal in the 51st minute, but Devon Sandoval tied it in the 77th minute by grabbing a loose ball thanks to a defensive mistake by the Revolution.
New England had a chance to tie in stoppage time, but Nick Rimando was able to stop a penalty kick taken by Saer Sene.
The Revolution fell to 2-4-3 and remained in seventh place in the Eastern Conference.