Chris Kunitz, acquired by the Penguins in a trade with Anaheim Thursday, had a goal and an assist in his Pittsburgh debut.
The Penguins improved to 4-1-1 since Dan Bylsma was named interim head coach. Marc-Andre Fleury earned the win with 41 saves.
Pittsburgh again played without captain Sidney Crosby, who suffered a groin injury Sunday. He was held out of Friday's game after trying to go through a morning skate.
Chicago lost its third straight despite Toews producing the first hat trick of his NHL career. The Blackhawks came from two goals behind twice and forced the overtime when Dave Bolland scored with 4:45 to play in the third period.
Cristobal Huet opened the game in goal for Chicago and let in four of 22 shots through the first two periods. Antti Niemi stopped the first five shots he saw in relief before surrendering the game-winner to Malkin, who leads the NHL with 61 assists and 89 points.