Jackson Goncalves looked to have secured a point on the road for Toronto when he scored in the 88th minute but RSL hit back straight from the restart, with Jordan Allen heading home from Javier Morales' cross.
The win took the Utah-based club from the bottom of the Western Conference to fifth with five points, one behind third-placed San Jose Earthquakes.
Luke Mulholland opened the scoring for RSL seven minutes before half-time, timing his run to the back post perfectly to nod Morales' cross into the net.
Goncalves levelled the score late in the second half on a counter-attack, just after Olmes Garcia wasted a chance for the hosts at the other end.
But from the kick-off, RSL attacked down the right and again Morales provided the decisive pass, as Allen secured victory for his side.
In Chicago, the Fire notched their first points of the campaign, with Adailton scoring in a 1-0 win over Philadelphia Union.
The Brazilian defender sent a glancing header past Philadelphia goalkeeper Rais M'Bolhi from Harry Shipp's free-kick in the 37th minute.
Philadelphia had midfielder Fred sent off in the second half.
Chicago rose from bottom in the East to eighth, level with Toronto (seventh) and Columbus Crew (sixth) on three points.
The Fire had lost their opening three games of the season.
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