The Colombian forward came off the bench to have a major say at Rio Tinto Stadium as Jeff Cassar's men climbed above Dallas and back into second in the Western Conference.
Issey Nakajima-Farran was sent off in the 65th minute for the Impact before Garcia stepped up to lead his team to victory.
It was Montreal's fourth straight loss and leaves them bottom of the Eastern Conference.
Englishman Luke Mulholland gave the hosts the perfect start with his third-minute opener, volleying in from inside the area after a corner.
Hassoun Camara levelled for the Impact in the 32nd minute, placing an effort into the bottom corner from a Calum Mallace pass.
Nakajima-Farran saw red soon after the hour-mark when he flew into a dangerous challenge on Christ Schuler near the halfway line.
The Canadian's dismissal would prove costly.
Garcia, introduced just before the hour-mark, restored Real Salt Lake's lead with a tremendous header from a Javier Morales cross in the 70th minute.
The 21-year-old sealed the win and his brace in additional time, taking a Morales pass before firing into the bottom corner.
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