In the third round of the shootout, Kane skated in and deked to the forehand before stuffing the puck in past the outstretched right pad of Marc-Andre Fleury.
Tyler Kennedy was the last hope for Pittsburgh, but Corey Crawford made a stop on the lifted backhand for the win.
Patrick Sharp and Bryan Bickell each had a goal while Crawford stopped 24 shots for the Blackhawks, who had dropped three of four coming in.
Brett Sterling and Matt Cooke each scored for the Penguins, who have lost three of their last four. Fleury finished the contest with 29 stops.