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.
NBC reportedly holds celebs hostage to Jimmy Fallon's show
Boston schools pull out free condoms over wrapping complaints