The Blackhawks are mired in a season-long, five-game losing streak and have dropped seven of their last eight.
Dwayne Roloson made 39 saves during regulation and overtime and was perfect in the shootout to earn his 24th win of the season. He has been victorious in two straight games after losing three in a row -- all in overtime.
Chicago never led in the game, but came from behind four times. Martin Havlat produced the only goal of the third period to create a 4-4 deadlock.
Edmonton advanced to 79 points, one behind Columbus for the sixth spot in the Western Conference.
Chicago remained in fifth place with 85 points.