Bryzgalov stopped all 24 shots he faced over the first two periods while protecting a 2-0 lead, and then held Boston at bay down the stretch to improve to 14-14-3 on the season.
Nathan Horton scored for the Bruins, who hold the fourth seed in the East.
Tuukka Rask turned aside 19-of-21 shots for Boston.
'SNL': 'Anchorman 2' cast, One Direction sing 'Afternoon Delight' [VIDEO]
Wisconsin business offering 'therapeutic cuddling' forced to close