The Bruins won their sixth straight at home and for the seventh time in the last eight games. Boston's last regulation loss was Oct. 30 in Calgary.
After falling behind 4-2 with 7:23 remaining in the first period, the Bruins scored five unanswered goals. Savard figured in on four of them, giving him 600 points in his career.
Savard closed the gap to 4-3 before the end of the first period, and Chara scored a pair of power-play goals sandwiched around Kobasew's second of the game as the Bruins took a 6-4 lead after two.
Kobasew seemed to deflate Buffalo when he scored a bizarre goal from behind the Sabres net. His shot fell off goalie Ryan Miller's back for Boston's first lead of the night.
Buffalo has dropped three straight and four of five. Miller allowed seven goals on 20 shots.
Miller and Bruins goalie Manny Fernandez struggled early, with Buffalo jumping to a 4-3 lead in the first 13:08.
Jason Pominville, who also added two assists, gave Buffalo a 1-0 lead when he hit a backhand shot over the left shoulder of Fernandez 1:41 into the first period.
Kobasew briefly tied the game just over a minute later, but Derek Roy and Thomas Vanek scored goals 29 seconds apart to give the Sabres a 3-1 lead 4:58 into the game.
David Krejci responded for 30 seconds later to cut Boston's deficit to 3-2, but Vanek notched his second goal of the night to give the Sabres a 4-2 lead with 7:23 remaining in the period.
Vanek has 15 goals after beginning the night tied for the league lead with Washington's Alexander Semin.
Patrick Lalime relieved Miller after Phil Kessel gave the Bruins a 7-4 lead 1:16 into the third period.
Notes: Bruins forward Marco Sturm missed the game with an upper body injury. ... Miller has allowed 11 goals in the last two games. ... The Bruins' Patrice Bergeron scored his 200th NHL point with his first of two second-period assists. ... Krejci and Matt Hunwick each had a pair of assists for the Bruins. ... Pominville has scored goals in four straight...Next up for Boston are the Florida Panthers, Friday night in the TD Banknorth Garden. You can find tickets here.