Boston rested eight starters, including Zdeno Chara and No. 1 goalie Tuukka Rask.
"We had a real tough opponent, and for the most part I thought we handled it OK," Bruins coach Claude Julien said. "For us it was just about playing a solid game."
While Brodeur didn't have a lot of work against the Boston lineup that included four players called up from the club's Providence AHL affiliate, this was a love fest for the player who led the Devils to three Stanley Cup titles and five appearances in the championship round.
He was cheered from the opening introductions, and every save brought chants of "Marty! Marty!" Toward the end, the crowd just chanted his name.
Zajac broke a 1-all tie at 3:52 of the final period. He got inside position on Matt Bartkowski in front of goalie Chad Johnson and redirected a pass from Jagr into the net.
Zidlicky stretched the lead to two with a power-play goal that Jagr also helped set up.
Boston managed to take some of the enjoyment out of the closing seconds when Marchand scored a power-play goal to make it a one-goal game.
"If this is his last game, it is (cool) to have scored," Marchand said. "I should have (grabbed) the puck."
The Devils outshot the undermanned Bruins 24-9 in the first two periods, but the score was tied 1-1.
Zidlicky gave New Jersey the lead 7:12 into the game. The defenseman joined a rush late and took a pass from Zajac entering the Bruins' zone.
He skated down the right side, went around the net and beat Johnson with a wraparound inside the post for his 11th goal.
Boston only had five shots in the period but the last one tied it on a power play. Marchand sent a pass from the right circle to Carl Soderberg in the opposite circle. He quickly found Eriksson with a pass at the right corner of the net for a slam dunk.
The Devils announced during the game that coach Pete DeBoer will return next season.
NOTES: Marchand played in his 300th game with the Bruins. ... The Bruins, the Presidents' Trophy winner for the best regular-season record also rested Jarome Iginla, Patrice Bergeron, Milan Lucic, David Krejci, Daniel Paille and Chris Kelly. They recalled forwards Craig Cunningham, Justin Florek, Alexander Khokhlachev, and Matt Lindblad from Providence.