Thomas was especially busy in the final period as the Canadiens frantically worked for equalizer. He turned aside 15 shots en route to his 29th career whitewash and third shutout of the season.
Andrew Ference got the game's only goal in the first period and the Bruins extended their longest winning streak since a 10-game run during the 2008-09 season.
The streak has put the defending Stanley Cup champions at 12-7-0 after beginning the season 3-7-0.
Carey Price turned aside 17-of-18 shots for the Habs, who swept the Bruins in a home-and-home series earlier this season.