The Bruins took a 1-0 lead in the best-of-seven Eastern Conference semifinals. Game 2 is Monday night in Boston.
With the Flyers due to receive a penalty in their own end, Savard got the puck at the right circle and slapped it past goalie Brian Boucher and under the crossbar.
Savard was injured on a blindside hit from Matt Cooke on March 7 and hadn't played since.
Tuukka Rask stopped 32 shots for Boston, and Miroslav Satan and Patrice Bergeron each had a goal and an assist.
Boucher stopped 41 shots, and Mike Richards had a goal and two assists for the Flyers.
Dennis Wideman had three assists for Boston, which took a 2-0 lead in the first 13 minutes and still led 4-2 with under eight minutes left. Richards cut the deficit to one goal with 7:23 to play, then Danny Briere outmuscled two defenders to go in alone on Rask and tie it with 3:22 left.
Boston had several good chances early in the overtime, and Philadelphia had one with 15:33 left when Rask stopped Daniel Carcillo on a breakaway.
The game was a rematch of the New Year's Day Winter Classic, and a rare second-round matchup of two teams that needed to win on the final weekend just to reach the playoffs. Boston beat the third-seeded Buffalo Sabres in the first round in six games, and Philadelphia upset the second-seeded New Jersey Devils in five.
When the top-seeded Washington Capitals lost their first-round series to Montreal, that left sixth-seeded Boston with home-ice advantage in the conference semis against seventh-seeded Philadelphia.
Boston and Philadelphia hadn't met in the playoffs since 1978, when the Big Bad Bruins beat the Broad Street Bullies in the second round for the second straight year.
Neither team has won the Stanley Cup since the '70s.
One of them will reach the conference finals.
The Flyers never led in the game, but they never let it get away from them, either.
They fell behind 2-0 in the first on goals from Steve Begin and Bergeron. Ryan Parent scored for Philadelphia to cut the deficit to one goal in the second, and after Satan made it 3-1 for Boston, Chris Pronger made it a one-goal game with 4:12 left in the period.
It was still 3-2 when David Krejci dug a puck out of the corner, leaving it for Milan Lucic before heading to the slot. Lucic got him the puck, Krejci did a little stickhandling to force Boucher to commit and then beat him with 12:35 left in the game.
It stayed that way until there was 7:23 left in regulation, when Richards scored a power-play goal to make it 4-3 a few seconds after Rask was knocked down in the crease by Scott Hartnell.
With 3:12 to play in the third, Briere split through Wideman and Matt Hunwick to go straight in on Rask, who stopped the first shot but left it there for Briere to score on his own rebound.
Notes
Satan has a point in four consecutive playoff games. … The Flyers were without leading goal scorer Jeff Carter (33 goals, 28 assists) and Simon Gagne (17, 23), who both have injuries with their right feet. … Bruins LW Marco Sturm left the game in the first shift favoring his right leg. He couldn't even get to his skates to leave the ice until a trainer came out to help him at the first whistle.