Saborio scored in the 32nd minute when he pressured Marvell Wynne and the Rapids defender passed the ball back to goalkeeper Matt Pickens, who was forced to clear it when Fabian Espindola hustled after it.
Espindola got a foot on the clearing try, and Saborio tapped it into the net for the decisive score.
Will Johnson added an insurance tally in the 90th minute for Salt Lake (13-7-3), which pulled to within one point of the Western Conference-leading San Jose Earthquakes.
The Rapids (7-14-1), meanwhile, fell further out of the playoff picture with the loss.
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