Simmonds snapped a tie in the third period with his 16th of the season, sparking the Flyers to the second-half start they needed as they make a playoff push.
Brayden Schenn also scored for the Flyers. Matt Read added an empty-netter in the final seconds and Steve Mason stopped 30 shots.
Andrei Markov and Jeff Petry scored for Montreal.
The Flyers have 15 games in February - Tuesday marked the first of eight in 13 days - and they entered five points out of an Eastern Conference wild-card spot. That's certainly enough of a load for any team. But this could be the month that determines if Philadelphia is playoff-ready or still another season or two from contending for the Stanley Cup.
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The Flyers play six games against their Metropolitan Division rivals and 10 against teams in the East. They three sets of back-to-back games during that span.
Under rookie coach Dave Hakstol, the Flyers are trying to make the playoffs for the second time in four seasons.
The Canadiens have stumbled since a strong start and scored only 48 goals (1.92 per game) since December - a steep drop from the 3.52 they averaged before the season went south.
By their standards, the Canadiens went on a scoring spree Tuesday, wiping out a 2-0 deficit by the third period. Markov scored his third goal of the season when he knocked in a wild rebound off the boards with 1:42 left in the first.
Petry scored 2:30 into the second from the circle to make it 2-all.
Simmonds saved the Flyers at the end after putting them on the board in the first.
Philadelphia grabbed a 2-0 lead in the first by getting power-play goals from Simmonds and Schenn, who had an assist on Simmonds' 15th of the season.
"I went to the net with my stick on the ice and Brayden made a great pass for a tap-in back door," Simmonds said.
The Flyers have power-play goals in five straight games.
The Canadiens played without All-Star Game MVP John Scott. He remained stuck in the minors with Montreal's AHL affiliate, the St. John's Ice Caps, even after his two-goal effort and feel-good story made him the hit of All-Star weekend.
NOTES: Flyers backup goalie Michal Neuvirth is out seven to 10 days with a lower-body injury. Anthony Stolarz was recalled from the AHL. ... The Flyers will play April 10 at the New York Islanders in a game rescheduled because of the recent snowstorm on the East Coast. ... Flyers D Radko Gudas received a game misconduct for a hit on forward Lucas Lessio.