"I just stayed with them and got a good gap, and then went from there," said Niemi, who made his first start of the season because Carey Price had the flu.
Paul Byron and Jonathan Drouin scored on Montreal's first two shootout attempts against Casey DeSmith.
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"I never faced him, or he never faced me, so I went to my go-to move there," Drouin said.
Tomas Tatar had two goals and an assist for the Canadiens (2-1-1).
DeSmith made 37 saves in his second straight start for the Penguins (2-1-1), who played their first road game.
"I thought he was terrific," Penguins coach Mike Sullivan said.
Pittsburgh was penalized for too many men 47 seconds into overtime but Montreal did not get a shot on the ensuing power play.
Canadiens forward Max Domi hit the post with 14 seconds remaining.
"That was wild, a really exciting game, obviously a fun place to play," DeSmith said. "This place is wild so it was an exciting one for the fans and I'm happy we got a point."
Phil Kessel scored his fourth goal in two games to tie it at 3-3 after Pittsburgh blew a 2-0 lead. Kessel, who scored a hat trick in a 4-2 win against the Vegas Golden Knights on Thursday, tied the score on the power play at 11:14 of the second period.