Sutter took a pass from Simon Despres on a rush, stepped around Max Pacioretty and beat Carey Price with a high shot to help Pittsburgh end a two-game losing run and avoid being swept on a three-game road trip.
They fell short of making a winner of coach Michel Therrien in his first game against the Penguins since he was fired by Pittsburgh in 2009.
Montreal outshot Pittsburgh 39-26 in a wide-open game with shaky goaltending at both ends as the Penguins opted to go with Vokoun over Sorel, Que., native Marc-Andre Fleury in goal.
A fast-paced first period saw Montreal draw first blood as Plekanec was on the doorstep to put in the rebound of Tomas Kaberle's shot from the side boards at 5:41.
The Penguins tied it on a power play at 19:07 as Sutter broke into the zone and saw his pass come back to him off Alexei Emelin's skate to beat a fooled Price.
Brendan Gallagher's charge to the net set up Pacioretty's seventh goal in his last seven games 4:14 into the second frame, but the Penguins answered with three straight goals.
Crosby made a deft move behind the net to set up Kunitz at the goalpost for his 10th at 8:29 and Cooke saw a long shot sail past a screened Price only 31 seconds later.
Montreal defenceman Josh Gorges tipped a puck onto the onrushing Cooke's stick for a goal from the high slot at 13:05.
But Montreal answered as Gionta put his stick between his legs to deflect Francis Bouillon's shot at 17:37. An ill-advised icing set up a face-off in the Penguins zone with seven seconds left in the period, and it was Gallagher again doing the work to set up Subban at the side of the net to tie it with less than a second on the clock.
Desharnais put in Emelin's rebound 5:25 into the third frame, but Kunitz one-timed a Crosby pass for his second of the game at 8:33 and Crosby put the Penguins ahead as he roofed a loose puck at 10:24.
Only 30 seconds later, Vokoun waved at Gionta's long shot to tie it at 6-6.
Notes: Crosby played his first game at the Bell Centre since Nov. 26, 2011. . . Brandon Prust played his 300th career game. . . Montreal called up centre Gabriel Dumont from AHL Hamilton late Friday. He was a healthy scratch along with Yannick Weber. . . Paul Martin, one of Pittsburgh's top defencemen, sat out with a lower body injury, while Zach Boychuk and Robert Bortuzzo were scratched.