Alvarez struck just before halftime, beating TFC goalkeeper Joe Bendik to the far post on a shot fired from just outside the box.
The victory was the sixth straight without a loss for Salt Lake (10-5-3), ensuring they would retain at least a share of the West's top spot throughout the weekend's play at 33 points.
TFC (2-8-6) saw its undefeated streak of three consecutive matches snapped and remained without a home victory.
Video of Victoria’s Secret models trying to 'twerk' hits Instagram
Exploding whale video goes viral on Internet