Patrice Bergeron scored an empty-net goal for the Bruins with 1:52 left.
Bruins goalie Tuukka Rask allowed a quick goal at the start, but finished with 34 saves. The Bruins can complete the sweep in Game 4 in Philadelphia on Friday night.
Wheeler and Satan scored 94 seconds apart in the first period to wipe out the Flyers' lead, and the Bruins never looked back. They won the first two games of the series at home - and the Bruins might not play in Boston again until the Eastern Conference finals.
Arron Asham scored for the Flyers.
The Flyers' first home playoff game since April 20 had an unusual vibe from the start. There were large patches of empty seats - mostly in the upper deck - and the normally rocking 20,000-plus was quiet from the opening faceoff.
Perhaps they sensed something.
The Flyers did give their fans a quick jolt, scoring first when Asham flipped the puck under a sliding Rask's glove only 2:32 in. It did more than give the Flyers the first lead of the game - it was their first lead of the series.
And their last one of the night.
The Bruins took over from there, even as injuries forced center David Krejci and Adam McQuaid out of the game. Krejci was leveled on a crushing hit from Flyers captain Mike Richards that actually led to Boston's go-ahead goal.
The loose puck was corralled by Milan Lucic, who got it to Satan for his fifth goal of the postseason and a 2-1 Boston lead.
The Bruins were outshot by a 2-to-1 margin most of the game. The Flyers had plenty of open looks, but they couldn't convert any rebounds against Rask. Rask stopped all 15 shots in the second period, including two Philadelphia chances on the power play. The Bruins defense did a fantastic job of shot blocking in front.
Unlike the Flyers, Boston was able to convert at least one power-play chance. Recchi, a former Flyers star, scored his 54th career playoff goal to make it 3-1.
The Bruins never gave the Flyers - or their fans - a chance to get going in the first period. The Flyers seemed to overcome their faceoff woes when they won one, only to quickly lose the puck in the corner. Wheeler deflected the puck off his stick past a startled Brian Boucher to make it 1-1. Satan followed with a forehand-to-backhand goal that dropped the Flyers into a deep hole.
Philadelphia has never won a series when trailing 3-0 (0-6). Only two NHL teams have recovered from such a deficit and advanced.
Hard to believe now this is the same Bruins team that lost 10 straight games in one stretch this season. They didn't clinch a playoff berth until their next-to-last game.
None of that matters now.
NOTES: The Flyers are 31-31 in Game 3s. ... The Flyers have never won a playoff series when trailing 0-2 and returning home to play Games 3 and 4. ... The Bruins are 16-0 when they lead a best-of-seven series 3-0.