The game was scoreless until the 59th minute with Alvaro Saborio broke the drought on a header. He added another tally in the 76th, only a minute after Matt Hedges had netted the equalizer for Dallas.
FCD (3-8-4) pulled even again at 2-2 in the 86th when Blas Perez got a shot though the fingers of Salt Lake goalkeeper Kyle Reynish.
That set up the decisive marker by Borchers, who was left unguarded 8 yards out and had plenty of time to line up a shot and fire it into the net for RSL (9-3-2), which stretched its unbeaten streak to six games.
Dallas is winless in its last nine contests.