Mitchell tied it with 1:40 left in the first, exploiting a rare Chicago coverage mix-up. Mitchell skated alone to the right side of the net, took a quick pass across the crease from Chuck Kobasew and lifted a backhand past Emery.
Varlamov stopped Patrick Kane on a 2-on-1 break and Carcillo on a point-blank chance early in the second.
Kobasew missed on a breakaway at 6:11 of the second moments after he jumped back on the ice from the penalty box.
Duchene put Colorado ahead 2-1 with 6:43 left in the second, moments after Varlamov made a point-blank pad save on Sharp.
Duchene streaked down the left side, slipped past Seabrook and took a pass from P.A. Parenteau. Duchene fired from a sharp angle near the goal line, but the puck struck Emery and slipped in under his right arm.
Toews scored at 2:19 of the third to tie it 2-all. He moved down the right wing, then cut to the net around Ryan O'Reilly. Toews skated across the crease — behind both O'Reilly and Jamie McGinn — and banked in a shot off the left post.
O'Reilly and McGinn are forwards who got caught as the two men back during the Colorado power play.
"You have a power play and you give up a chance," Sacco said. "It's a good play by a real good player on the other team, but I want to watch the tape again.
"I'm pretty sure O'Reilly got his stick slashed out of his hands (by Chicago's Dave Bolland). It led to a 1-on-1 situation. If it did, it's a bad non-call, but there's nothing I can do about it now."
Carcillo's game-winner was his first goal since returning from a knee injury on Feb. 22.
"We had a big breakdown at the end of the game," Sacco said.
NOTES: Blackhawks coach Joel Quenneville offered a postgame injury update. He said Hossa "is close to playing" and might be ready Friday at Colorado. Quenneville said the team would know more about Shaw on Thursday, but Sharp could be out longer and "may get some time." ... The Blackhawks finished the 2011-12 regular season with a 3-0-3 spurt before losing to Phoenix in the first playoff round. ... The Blackhawks assigned LW Brandon Bollig to the Rockford IceHogs of the AHL. Bollig had played in only two of seven games since Carcillo returned from his knee injury. ... Chicago RW Michael Frolik missed his second game with an illness. ... Colorado played its second game without injured RW Milan Hejduk (torso). D Erik Johnson (head) missed his 11th game and D Ryan Wilson (ankle) his 14th.