Philadelphia has a 3-1 advantage in the series and can eliminate the top-seeded Canadiens when Montreal hosts Game 5 Saturday.
It was the eighth goal of the playoffs for Briere, tying him for the post-season lead in that category with Detroit's Johan Franzen.
Briere's wrister came on the power play 30 seconds after Steve Begin went to the penalty box for interference.
R.J. Umberger added an empty-net goal with two seconds to play.
Umberger scored the game's first goal midway through the second period and Scott Hartnell gave Philadelphia a 2-0 lead 6:47 into the third.
The Canadiens' only victory in the best-of-seven series came in overtime.
Martin Biron made 36 saves for the Flyers.
2014: The Year in Music [PHOTOS]