Saku Koivu scored his first goal of the playoffs for Montreal. Carey Price made 19 saves.
Game 3 is Monday night in Philadelphia.
Umberger opened the scoring 5:53 in with his third goal of the playoffs. He sealed the win with his second goal of the game with 2:21 remaining in the third, shooting into a wide open right side after he batted the puck out of Price's glove.
Briere, who has been booed throughout the first two games at the Bell Centre, got his seventh goal of the playoffs 13:33 into the second to restore the Flyers' two-goal lead after Koivu scored on a power play late in the first.
Briere cut across the goalmouth and put a backhand under Price's pad and off the left post and over the goal line. Briere has been a constant target of Canadiens fans through Philadelphia's four games in Montreal this season - including two regular- season games - after he passed up a Canadiens contract offer to sign as a free agent with the Flyers.
Price was beaten on shots over his left shoulder twice in the first half of the opening period as Umberger and Carter scored goals 2:46 apart to give Philadelphia a 2-0 lead 8:39 in.
Umberger took a drop pass from Jim Dowd in the right corner and used Koivu as a screen when he put a wrist shot over Price's shoulder into the top right corner of the net for his third goal.
Carter made it 2-0 with his fourth goal, a power-play effort at 8:39 as he beat Price with a shot from the right side.
Koivu scored a power-play goal at 16:18 to cut the lead to 2-1 shortly after the Canadiens enjoyed a lengthy two-man advantage.
The Montreal captain reached around from behind the net to tuck the puck inside the right post, setting off a wild celebration by the crowd of 21,273.
Notes: Canadiens D Ryan O'Byrne was in the lineup for the third time in Montreal's ninth playoff game. D Patrice Brisebois did not dress because of a leg injury.
