Tim Thomas made 26 saves for the Bruins, who lost for the fifth time in 21 games.
Langenbrunner and Zach Parise scored to give the Devils a 2-0 lead after two, but Boston took its first lead on Dennis Wideman's slap shot with 6:30 left. New Jersey tied it on Patrik Elias' goal with 1:45 to play in regulation.
Boston's Marc Savard had a goal and an assist, and Phil Kessel had a pair of assists in his first game after missing six with mononucleosis.
The Atlantic Division-leading Devils, who had given up just six goals in five games, moved past Washington and into second place in the Eastern Conference, 11 points behind the Bruins.
Elias scored after the Bruins twice failed to clear the puck out of their zone in the closing minutes, crashing the net and tipping a pass from Brian Gionta past Thomas; a replay review confirmed he did not kick it in on purpose.
Langenbrunner gave the Devils a 1-0 lead with 4:59 left in the first period on a short-handed goal, putting the puck off both of Thomas' pads before it squeaked across the goal line. Langenbrunner assisted when Parise put a shot off Thomas' back from behind the net with 13:39 left in the second to make it 2-0.
The Bruins made it 2-1 with 17:40 to play in the third when Clemmensen went behind the net to play the puck but left it there for Chuck Kobasew, who swept it around and into the post. Kobasew got the rebound into the net, and Clemmensen gloved the puck out of the air, but the replay showed that it had crossed the line.
Savard scored his 18th of season 7:11 into the third, taking a pass from behind the net on the side, sliding it over the goal line, and wristing it between Clemmensen and the post to tie it 2-all.
Notes: Devils forward Jay Pandolfo missed his fourth straight game as a healthy scratch. ... Parise extended his point streak to five games. ... Savard has a six-game point streak. ... Before this season, two of Clemmensen's eight NHL wins were against the Bruins.
The Devils goalie also played in the new Boston Garden while at Boston College.