His fifth goal this season increased Boston's lead to 2-0 at 10:20 of the first period and made sure Boston never trailed.
Savard added an assist and Tim Thomas stopped 28 of 29 shots for the Bruins, who bounced back from an 8-2 thrashing at Montreal Tuesday to ease into the NHL all-star break with three wins in their last four games.
New York's lone goal was scored by Mike Sillinger at 6:45 of the third.
Mike DiPietro was beaten four times on 30 shots for the Islanders, who have dropped three of four.
Before the loss, they had won their previous four road contests.