With the Rapids trailing 1-0, Sanchez launched a hard shot that found the net for the equalizer.
Then in the 65th, Uruguayan got past George John and sent a cross to the goal that was accidentally tipped in by defender Matt Hedges as Gabriel Torres was in pursuit.
The victory gave the Rapids (12-8-9) sole possession of third place in the Western Conference with the season winding down.
David Ferreira scored for FCD (10-8-10), which remained on the outside of the West's conference picture.
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