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.
Chicago grabbed a 1-0 lead halfway through the first. Niklas Hjalmarsson sent a pass from the left point to the low left side for Jonathan Toews, who immediately whipped it out front for the easy shot over Fleury's glove by Sharp.
Pittsburgh tied the game while shorthanded at the 13:52 mark of the second as Maxime Talbot fired a saucer pass from the top of the right circle to the low left side where Cooke redirected it in.
The Blackhawks made it a 2-1 game 1:09 into the third after Bickell let fly with a wrister from the outside left circle that made its way past Fleury's glove.
"They got a lucky goal," said Cooke. "But we stuck with it and came back to tie the game."
The equalizer came with 3:18 to play in regulation when Kennedy blasted a shot on net that was stopped, but the rebound went to open ice and Sterling slammed it home.
"We came back pretty hard right after that, so I think that was the key for us tonight -- to not get down after they scored late," said Crawford.
Chicago plays in St. Louis on Monday...The Penguins, who went 1-2-1 on their four-game road trip, host Washington on Monday...Chicago has won the past two games against Pittsburgh...Play was delayed for several minutes with 11:50 left in the first period after a pane of glass fell out when a player was checked into the boards.