Chicago (4-7-3) extended its unbeaten streak to four games as it tries to dig its way out of an early-season hole.
Colorado (5-6-5) suffered its second straight loss after having gone six games without one.
Deshorn Brown scored in the 17th minute to put Colorado in front, but Mike Magee tied it 6 minutes later on a penalty kick. Chicago was awarded the penalty when Marvell Wynne was called for a hand ball in the area.
Berry's game-winning goal came from a cross by Jeff Larentowicz off a corner kick.