Jaroslav Halak made 23 saves for the Bruins (10-3-2), who have lost their past two games after winning five straight.
"I think it was our inability to win 1-on-1 battles, to defend areas of the ice, to give them access to our zone, to not keep forecheck situations alive or even create them," Boston coach Bruce Cassidy said. "I just thought they were winning the races, the 1-on-1 battles. We just didn't want to do what it took to sort of get pucks back and win pucks and hang on to pucks. And as a result, they came at us and were the better team and looked better."
Boston next plays in the Honda NHL Outdoors Sunday game against the Philadelphia Flyers at Lake Tahoe, Nevada.
Palmieri gave the Devils a 1-0 lead at 1:34 of the second period with an assist from Jack Hughes, and made it 2-0 with a shorthanded goal on a breakaway at 10:39.
They were his first goals since March 7, 2019.
"It's nice to kind of get the monkey off your back there," the forward said. "Jack made a great play, and it's just nice to contribute in that way."