Chicago swept a three-game homestand that included a five-goal rally in a 6-5 victory over Calgary Monday.
Barker's power-play goal was his second of the season and allowed Chicago to survive a goal by Edmonton's Denis Grebeshkov with just 57 seconds to play.
Antti Niemi had to make only 16 saves to get the win.
The loss went to former Chicago goaltender Nikolai Khabibulin, who allowed four goals on 38 shots.
Chicago's Patrick Sharp scored his fifth goal of the season just 51 seconds into the contest to help give the Blackhawks a 2-1 lead after one period.
Sharp has had at least one point in all six games this year.
Copyright 2009 by United Press International.
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