Kyle Palmieri scored for the Devils (8-11-2), who won for the second time in their past 10 games and the first in regulation since a 2-1 victory at the Bruins on Feb. 18.
Wedgewood made 18 saves in the third period in his second shutout this season and fourth in his NHL career in 30 games (27 starts). He had not played since a 4-3 shootout loss at the Buffalo Sabres on Jan. 30.
"We obviously have been on the bad side of things for a bit here," Wedgewood said. "Obviously, we addressed it this morning and talked about what we wanted to do defensively, and we accomplished our goal.
"We kept them outside for most of the night and any opportunities they did get, we tied up sticks and limited rebounds and just kind of took care of our own end first. And it paid off. It's a gutsy 1-0 win."
Tuukka Rask made 24 saves for the Bruins (13-6-3), who lost in regulation for the first time in four games (2-1-1).
"We had enough looks around the net to certainly generate a couple of goals tonight, I thought," Boston coach Bruce Cassidy said. "I thought a lot of pucks hit [Wedgewood]. I thought he made some good saves, obviously, especially in the third period.
"I think we did a little better job attacking with our forward group against their D as the game went on. I think we were settling for a little bit of low to high [earlier], they typically really converge toward their net, so that's a good outlet. And then as the game went on, I thought we could inside a little more. We did, but we didn't finish. You're not going to win if you don't put some goals on the board."
Palmieri scored at 15:23 of the third period when he redirected a shot from Pavel Zacha to make it 1-0. It was his first goal in nine games.
"It feels awesome," Palmieri said. "I think after this past week we took the opportunity this morning to really examine our game individually, as a team, and sometimes there were games over that homestand that we played well and played tight games and maybe deserved a little better or a closer result. But obviously, the game [Saturday] afternoon (a 6-3 loss to the New York Rangers) was a bit of a low point for our group as a whole, and I think it was time for us to take a look at the things that made us successful.
"I think coming on the road against a team like Boston, it's almost sink or swim. We had to go out there and play with urgency and compete. That's exactly what we did, and I think as a group we can be really proud of our effort tonight."
