Chicago's Ante Razov scored his first two goals of the campaign on a pair of penalty kicks while the Fire's Justin Mapp netted his first goal as a professional.
Beasley helped open the scoring in the sixth minute, taking the ball away from Colorado's Wes Hart along left sideline and attacking the goal.
Just as Beasley entered the penalty area, Hart attempted to knock the ball away, but instead undercut the midfielder's legs. A penalty kick was awarded by referee Brian Hall and Razov promptly gave the Fire a 1-0 advantage, sending a low shot into the left corner of the goal.
A turnover by Hart also led to the second Fire goal as Beasley swooped in to pick up the loose ball near midfield after Hart stumbled. Unchallenged as he bolted down the left wing, Beasley entered the penalty area and lashed a wicked left-footed blast into the top right corner of the goal.
Six minutes later, rookie Damani Ralph sprang Beasley down the left side again with a heel pass. Beasley slotted a pass across of the mouth of the goal to Mapp, who finished with a low shot to make the score 3-0.
Chicago pushed the margin to 4-0 in the 75th minute when Razov converted his second penalty kick of the game after Kelly Gray was pulled down in the area by the Rapids' Nat Borchers.
Razov became the third player in league history to score two penalty kicks in one match.