After spotting the Revolution a 1-0 lead, Saborio struck from 10 yards out on a Kyle Beckerman cross in the 33rd minute for the equalizer.
Then in the second half, the RSL forward headed a Javier Morales free kick inside the far post for the decisive tally.
The win allowed Salt Lake (7-3-1) to pull into a tie with San Jose atop the Western Conference with 22 points.
Blake Brettschneider scored for New England (3-6-0), which fell for the fourth time in five matches.
Notable deaths of 2014 [PHOTOS]