Booed by Montreal's fans since he passed on the Canadiens' bid to sign him as a free agent in 2007, Briere opened the scoring 4:37 in and put the Flyers up 5-1 with six seconds left in the second with his second goal of the game against Jaroslav Halak.
"Let's just say that it's easier to find the motivation to play," Briere said. "Obviously, having friends and family in the stands and everybody booing you, it gives you that little extra juice pumping in your veins, there's no doubt about it."
Briere completed his hat trick when he beat Carey Price on a penalty shot midway through the third for his 21st goal.
"All I was thinking about was the crowd booing me and in a sense it was a good thing because it kind of cleared my mind, gave me the chance to not even think about it, just let it happen," Briere said. "Coming down on Price I had a couple of other ideas and at the last second I just changed and it worked."
Michael Leighton made 26 saves for his second straight win over Montreal as the Flyers swept the home-and-home series in the final games for both teams prior to the Olympic break.
Though he is not currently on Canada's Olympic roster, Carter will travel as requested by Canada's executive director Steve Yzerman to Vancouver, where he will play for the team if Anaheim's Ryan Getzlaf is unavailable because of injury.
"I'm going but that's all I know," said Carter, who will make the trip Sunday with fellow Flyers Richards and Chris Pronger. "I really don't know what's going on so I don't want to talk about it too much."
Philadelphia won its fourth in a row as it completed its second straight home-and-home series sweep, including consecutive wins over New Jersey.
"Looking back, I think we probably would have been happy with a split in both games," Briere said. "But coming out with four wins, this is huge for us and it's a good way to set us up for after the break."
Halak stopped 12 shots in two periods for Montreal. Price replaced him to begin the third and made eight saves the rest of the way.
Canadiens coach Jacques Martin said his beat-up team needs "to take a mental break."
"I told them about the importance of the final stretch of 19 games," Martin said. "Right now we're in a playoff position, but we need to sprint to the finish over those final 19 games."
Richards made it 2-0 midway through the opening period with his 24th goal on a power-play. Carter, who scored twice on Price in Friday night's 3-2 win, beat Halak for his 27th at 15:50 to put Philadelphia up 3-0.
Gionta drew Montreal to 3-1 when he tipped Roman Hamrlik's shot past Leighton for his 17th goal 6:59 into the second.
Betts restored the Flyers' three-goal margin with a short-handed goal at 10:38. Betts drove in on a breakaway and fired a shot past Halak for his seventh goal, an unassisted effort that made it 4-1.
Briere got his 20th goal -- his second of the game -- at 19:54 when he deflected Chris Pronger's shot to put Philadelphia up 5-1.
Philadelphia's Darrell Powe was given a boarding minor 5:57 into the third for checking Tomas Plekanec into the boards from behind.
Gomez scored nine seconds into the ensuing power play to draw Montreal to 5-2.
Powe got a boarding major and a game misconduct with 58 seconds remaining Friday night for his hit from behind on Jaroslav Spacek.
Spacek, who left and did not return Friday, was back in Montreal's lineup Saturday night.
- Flyers C Ian Laperriere dropped Montreal's Ryan O'Byrne to end their fight off the opening faceoff four seconds in. "Last night was a chippy game at the end and he wanted to get his team going and I really respect what he did," Laperriere said.
- Canadiens D Hal Gill played his 900th game.
- Montreal D Andrei Markov missed his second straight game because of a lower-body injury. Markov is expected to play for Russia in the Olympics.