David Pastrnak had a goal and an assist, John Farinacci scored in his NHL debut, and Nikita Zadorov had two assists for the Bruins (33-39-10) in their season finale. Jeremy Swayman made 21 saves.
Boston failed to qualify for the playoffs for the first time since the 2015-16 season.
“It’s sad it’s over, obviously,” Pastrnak said. “That’s pretty much the only answer I can give you right now. It’s tough. We want to keep playing, I’ll leave it at that.”
Meier gave the Devils a 1-0 lead at 7:25 of the first period when his quick shot from the right circle beat Swayman to the far post.
Morgan Geekie tied it 1-1 at 8:43. Pastrnak made a cross-ice pass to Geekie, who was waiting at the top of the left circle for a one-timer that beat Allen to the short side.
The Bruins took a 2-1 lead on Pastrnak’s 43rd of the season at 29 seconds of the second period. After a give-and-go with Elias Lindholm at the offensive blue line, Pastrnak split two defenders and scored with a backhand.
Stefan Noesen tied it 2-2 on the power play at 4:07, shoveling the puck in from the crease after Swayman couldn’t cover it.
Simon Nemec gave the Devils a 3-2 lead 30 seconds later. His wrist shot from the high slot looked like it was going to sail over the net when Swayman attempted to play it with his blocker and it ricocheted into the net.