Kimmo Timonen and Matt Read also scored for the Flyers, who made the post-season for the 16th time in 17 years.
The win gave Philadelphia 96 points, good for the fifth seed in the Eastern Conference.
Ilya Bryzgalov made 23 saves and assisted on Briere's second goal as the Flyers logged their fifth win in seven games.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys