Jean-Sebastian Giguere allowed two goals on 31 shots for the Avalanche, who ended a five-game losing streak and consigned the Blackhawks to their sixth loss in a row.
"We have to get in a better position to turn things around," Chicago defenseman Duncan Keith said. "We have to start outworking the other teams."
After Sea brook opened the scoring 31 seconds into the second period, Colorado took a 2-1 lead on goals by Peter Mueller and Jones.
Kane tied the score 2-2 on a backhander at 6:14 of the second period, but Colorado took control with third-period scores by Gabriel Landeskog and Jones plus an empty-net goal by Kyle Quincey.