Savard's ninth goal this season came during Boston's three-goal first period.
Daniel Paille (4), Vladimir Sobotka (4) and Michael Ryder (9) (power play) also scored goals. Net-minder Tim Thomas yielded four goals on 29 shots for the Bruins, whose two straight victories followed a four-game losing streak.
Maxim Afinogenov's goal with two assists led Atlanta.
Bryan Little, Ilya Kovalchuk and Evander Kane also scored, but goalies Ondrej Pavelec and Johan Hedberg combined to give up six goals on 30 shots for the Thrashers, who suffered their third straight loss.
Pavelec was beaten three times on eight shots in just under 11 minutes.
Ryder scored the lone power-play goal on nine combined chances.