Elias broke a 1-1 tie with 1:26 left in the middle frame, helping New Jersey (15-6-1) snap a three-game winless skid. He redirected Andy Greene's wrist shot past Ottawa's Brian Elliott for his first goal of the season.
The Devils also received a goal from Niclas Bergfors and Jamie Langenbrunner's empty-netter to win their fifth straight on home ice. Jacques Lemaire prevailed in his 400th game behind the Devils' bench.
Elias, the Devils' all-time leading scorer, now has a goal and five assists in his last four games.
"We got it deep there and got a pretty good cycle," Elias said. "A nice pass to Greener there that opened up the space, and I just came from behind and snuck in. Greener saw me coming in, and just a little quick wrister. Good tip on that."
Elias missed the first 13 games of the season because of offseason groin surgery, then went his first four games without a point. He had to wait until his eighth game for his first goal, but said it never weighed on him.
"It's going to come eventually," he said. "When you have injuries, and things like I did, you have to be patient, you have to take your time and not really focus on just scoring or doing everything that you can't at the beginning. It's a work in progress. It takes time. I feel like I'm taking the next step every game."
For Elias, that progress has started showing up on the scoresheet.
"I feel more comfortable," he said. "I'm starting to make plays, getting chances, getting shots, so that's a good, positive sign. Hopefully I can keep it going. On the other hand, I still don't feel 100 percent, which is a good thing. Hopefully, I will, and the good thing is, I keep making progress slowly and as long as I'm OK to play the next game, that's all I can ask for."
Greene assisted on New Jersey's first two goals and was happy to see Elias contributing in the goals column.
"It's huge," said Greene. "He's a big part of this team, obviously, and we need him. You can see every game he's kind of getting better and better. It won't be long until hopefully he's right there where he thinks he should be and needs to be."
Brodeur made 12 of his 24 saves in the third, and was named the game's First Star. He got a stick on Chris Kelly's backhander after Kelly collected a defensive-zone turnover by Dean McAmmond five minutes into the final frame.
With nine minutes remaining, Brodeur denied Kelly's redirection from the slot, then fought off Jarkko Ruutu as he jammed away at the loose puck to protect the 2-1 lead.
"They did have a couple of good chances, a couple of breakdowns," Brodeur said. "They had a couple of high tips, and I was able to be in good position. The puck was hitting me."
The Devils improved to 6-4-0 at Prudential Center. After Friday's noon puck drop in Boston, they return to play nine of 10 in New Jersey.
"It's a huge advantage to play at home," Brodeur said. "We have to take it somehow. It's not an easy thing to do; it's easy to say. But I think we have to play a certain way in our own building. We're playing to have all these points, and that's going to translate into home-ice advantage, hopefully, in the playoffs, if we do get there. It's important to learn to play at home with the way Jacques likes to coach at home and do the things that he wants us to do."
Lemaire didn't think much of reaching 400 games with the Devils, but the milestone came in an important bounce-back win for his club.
"I was afraid of this game," he said. "I knew that Ottawa was playing good, they had piled up a few wins there. Before the game I said, 'We better win this one, because the teams that are coming up won't be easy either.' We got a chance, they had a late injury (to Mike Fisher), (Alexei) Kovalev didn't play, so you have to take advantage of all this."
The contest was tied 1-1 after the first period. Bergfors drew first blood with his sixth of the season before Milan Michalek countered for Ottawa.
Greene fired a dump-in that caromed off the glass supports and bounced to Bergfors in the slot. He tucked the puck around Elliott's left pad, ending a five-game goal drought at 7:58 of the first period.
"I was just trying to fire it in there and get our forecheck going," Greene said. "Luckily it hit that glass partition there and bounced right out in the slot to Bergy. That's why you throw it up on the glass there. You never know what's going to happen."
Michalek answered by tipping Jesse Winchester's wrist shot past Brodeur for his 11th of the season at 12:34.
Elias put the Devils on top for good at 18:34 of the second. Langenbrunner passed to the right point where Greene floated one toward the Ottawa net as Elias crossed in front.
"Jamie made a good pass through the seam there, and I saw Patrik come out of the corner," Greene said. "I was just trying to shoot for a tip, and he got a stick on it and made a great tip."
Langenbrunner tallied his fifth of the year into an empty net, and finished with a goal and an assist. Zach Parise's assist on the goal extended his points streak to eight games (7g-6a).
NJD NOTES Travis Zajac briefly left the ice in the second period after taking a shoulder to the face from Ottawa captain Daniel Alfredsson. After the game, he had a small cut on the bridge of his nose.
"I got an elbow or a shoulder in the face," Zajac said. "It doesn't feel good, but it's just a little bit of a bloody nose. No stiches. Just going to make me look prettier, I guess."
• Andrew Peters' second-period hit on Alexandre Picard near the Devils' bench wound up sending the Ottawa defender to the dressing room. Picard eventually returned.
Peters came together with Ottawa heavyweight Matt Carkner immediately after the hit, and the two were whistled for matching minors.
"In an 82-game schedule, sometimes those hits aren't always there," Peters said. "When your job is to be sound defensively, you can't be running around looking for hits and getting out of position. A couple of hits were in my area and I just did what every hockey player would do, which is finish my check."
• Tyler Eckford saw double-duty in his third NHL game. He skated as a forward at even strength and manned the point on the power play. The Devils went 0-for-4 with the man advantage. Almost three minutes of Eckford's 7:57 came on the PP.
"I just kept it basic and did our role," Eckford said. "It felt good."
Though Eckford has experience at forward, it was a new challenge to play both positions in the same game.
"I've never seen it either, but that's the situation that's going on, and that's just the way it has to be," he said.
• Defenseman Matt Corrente, who debuted at forward last Saturday, was moved back to the blueline.
"Corrente played really well tonight," Lemaire said. "For his first game (on defense), he was poised. He did some plays that five-year (veterans) can do. I was impressed with the way he played. He played good minutes (8:54) too."
• Rob Niedermayer, who skated with the team Wednesday morning, will not travel to Boston. He has missed the last nine games with an upper body injury.
1 - 0 NJD
1 - 1 Tie