Savard praised Bruins coach Claude Julien for an inspiring talk before the game as Boston rebounded from a 5-1 loss to Montreal on Friday.
"Claude's pre-game speech tonight was probably one of the best I have ever heard," Savard told reporters.
"It really fired us up early. It was special. So I think the guys reacted and gave it a good 60-minute effort."
Marco Sturm opened the scoring for the home side at 5:28 in the first period and Savard made it 2-0 less than 40 seconds later.
Netminder Tuukka Rask made 31 saves as the Bruins held Toronto's Phil Kessel, Boston's leading goal scorer last season, to two shots and no goals in his first game against his old club.
"We didn't play well. I didn't play well," said Kessel, who was booed throughout the game.
Niklas Hagman and Mikhail Grabovski scored Toronto's consolation goals, both coming in the final five minutes.
(Reporting by Gene Cherry in Salvo, North Carolina. Editing by Patrick Johnston To query or comment on this story email firstname.lastname@example.org)