Olmes Garcia scored his first two goals of the season in the 70th minute and again in stoppage time to move Salt Lake within six points of conference-leading Seattle.
The hosts opened the scoring in the third minute when Luke Mulholland hammered in a deflected corner.
Montreal equalized when Hassoun Camara rolled the ball inside the far post in the 31st minute.
Montreal's Issey Nakajima-Farran was shown a red card in the 65th minute after a studs-up tackle of Chris Schuler.
Real Salt Lake capitalized five minutes later when Garcia headed home a cross from Javier Morales and the duo combined again deep into stoppage time.