The Bruins built a 4-1 lead before the Kings rallied to make it a 5-5 game on Anze Kopitar's power-play goal at 8:19 of the third, his second score of the night.
Savard scored on the power play less than two minutes later to put Boston back in front, and the Bruins then got goals from Milan Lucic and Chuck Kobasew, who scored into an empty net with 1:27 remaining to make it 8-5.
Patrick O'Sullivan scored for the Kings with five seconds left as the teams combined for seven goals in the final period.
Boston is opening its season with a five-game western road trip and this was the fourth contest. The Bruins have split the four games.