The midseason acquisition scored the equalizer and forced the winning own goal as Colorado strengthened its playoff positioning.
The victory gave Colorado a one-point lead on the LA Galaxy for third place in the Western Conference. Dallas remains on the outside looking in at a playoff spot, trailing fifth-place Portland by two points.
Dallas broke the deadlock in the 51st minute. Making an overlapping run on the left flank, Jair Benitez ran onto Fabian Castillo's pass and hit a low centering feed that David Ferreira managed to poke home.
Colorado leveled the match eight minutes later. After Je-Vaughn Watson headed an ill-advised clearance back across the box, Sanchez from a tight angle hit a volley that beat Raul Fernandez.
And the Rapids went in front in the 65th minute. In possession on the left side of the box, Sanchez shook George John with a cut before hitting a pass in front of goal that deflected in off Dallas center back Matt Hedges.