The game was scoreless until the 56th minute, after which the team squads combined to score four goals in a 10-minute span.
Colorado's Atiba Harris scored in the 56th minute, and Perez responded with the first of his two goals 5 minutes later to forge a 1-1 draw.
Harris struck again for a Rapids in the 64th minute after finishing a cross from Chris Klute.
But Perez got the final say for Western Conference-leading Dallas (8-2-4), firing home a low drive from 20 yards out.
The Rapids (5-4-5) drew even with Los Angeles for fourth place in the West with 20 points.
Kate Middleton recycles dress at movie premiere
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need