Fleischmann tallied with 2:24 remaining to pull the Avs into a 5-5 tie and 60 seconds later stole the puck from Brent Seabrook behind the Blackhawks' net and fed Matt Duchene for the go-ahead tally.
Brandon Yip and Cody McLeod also scored while Craig Anderson stopped 29-of-34 shots for the Avs.
The loss was the third in five games for Chicago.
Troy Brouwer led the Hawks with two goals and one assist and Jack Skille, Jeremy Morin and Bryan Bickell each scored.
Corey Crawford allowed the two late goals on 19 shots after replacing Marty Turco in net early in the second period.