Tomas Plekanec, who scored Montreal's first two goals, snatched the puck away from Penguins' star Sidney Crosby inside the Canadiens' blue-line and went in on a two-on-one. He slipped the puck to Souray for a blast that gave Marc-Andre Fleury no chance.
Mark Streit also scored for Montreal (29-19-6), which moved one point ahead of Ottawa for fourth in the Eastern Conference, each with 54 games played.
Trailing 2-1 going into the third period, Montreal scored on its first two power plays of the game as Plekanec got his second of the match at 1:10 and Streit put the Canadiens ahead at 5:59.
But Michel Ouellet went to the net to tip in Ryan Whitney's pass on a power play to send the game into overtime at 17:26.
Crosby set up the 18th goal by rookie Jordan Staal and another by Whitney for Pittsburgh (26-18-8), which despite the loss extended its run of games with at least one point to 10.
Plekanec and Souray each had three points for Montreal. Plekanec has five goals in the last seven games, while Streit has three in his last four.
After a wild and sometimes nasty 5-4 shootout win by Pittsburgh on Thursday, the fast-paced rematch had good hitting and some minor shoving, but no incidents.
Canadiens coach Guy Carbonneau, angry with his team's listless play of late, scratched struggling wingers Sergei Samsonov and Alexander Perezhogin.
He put captain Saku Koivu on the checking line, going head-to-head with Crosby, and dumped Michael Ryder to the fourth line.
The changes went fine early, but the Canadiens encountered penalty trouble and Staal opened the scoring during a two-man advantage at 11:33. Montreal was handed the first six minors of the game.
David Aebischer then kept the home side in the game, making a smart glove save on Ouellet from the doorstep and seeing Crosby miss a wide-open net.
Plekanec beat Mark Eaton to Maxim Lapierre's rebound to tie the game 4:48 into the second frame, but Crosby faked a shot and slid the puck for Whitney to fire into an open side on a power play only 47 seconds later.
The sell-out crowd of 21,273 booed the Canadiens off the ice at the end of the second period, but Eaton was sent off 49 seconds into the third period and Plekanec then banged in Alex Kovalev's rebound to tie the match again.
Pittsburgh's second minor went to Evgeni Malkin, and this time Streit went to the net to jam Ryder's rebound in.
On Tuesday, Montreal remains at home to face Carolina while the Penguins return home to play Nashville.
The Canadiens began playing two afternoon games on Super Bowl weekend in 1990-91 and are 17-11-4 in those games.
Notes - Andrei Markov, Montreal's best defenceman for most of the season, sat out with a "lower body" injury . . . Little-used defenceman Janne Niinimaa and enforcer Aaron Downey were dressed . . . The Pens' Colby Armstrong, who injured a knee Thursday against Montreal, sat out a second game.