On the winning play, Brian Mullan collected a pass from Martin Rivero in full stride and hooked up with a wide-open Cummings, who slotted a shot into the net for his second goal of the season.
The Rapids padded their margin when Kamani Hill scored on his own rebound, and Colorado (3-1-0) won for the third time in four contests in the season's early going.
The Fire (1-1-1), meanwhile, suffered their first loss.
Chicago had its best chance in the 68th Dominic Oduro's turnaround shot was barely deflected away by Rapids goalkeeper Matt Pickens.
Notable deaths of 2014 [PHOTOS]