"If I was going to pick a player, I was pretty happy to see him go down on a breakaway," Devils coach Alain Nasreddine said of Hughes' goal. "That was a goal scorer's goal. He's got that speed to separate himself and was able to get that breakaway, and it was a big goal for him."
The top pick in the 2019 NHL Draft chipped the puck over goalie Craig Anderson's left shoulder on a breakaway for his first NHL overtime goal.
[WATCH: All Devils vs. Senators highlights]
"I wasn't really thinking of a move," Hughes said. "[Pageau] was [behind me], so I had to move up the ice pretty fast and really, that was my only play, to chip it far side."
Sami Vatanen had three assists, Nico Hischier, Miles Wood and Nikita Gusev also scored, and Mackenzie Blackwood made 20 saves for the Devils (13-19-6), who are on a three-game point streak (2-0-1).
Video: NJD@OTT: Gusev buries wrist shot for PPG
"I think we have more belief in our locker room," Hughes said. "The team's playing better, for sure, and we're hungry for points right now. We want to climb in the standings. We're not happy where we are."
Thomas Chabot, Nick Paul and Artem Anisimov scored, and Craig Anderson made 30 saves for the Senators (16-18-5), who have a point in five straight games (2-0-3).
"We found a way to get a point," Ottawa coach D.J. Smith said. "We didn't have the puck very much tonight. I didn't think we were very smart with it. We didn't break out very well. In saying that, we found a way to get to overtime, we played hard in the third, it's just that we have to play a little smarter."
Hischier tipped a Vatanen point shot on the power play to give the Devils a 1-0 lead at 8:58 of the first.
Video: NJD@OTT: Hischier deflects home opening PPG
"He's got a shooting mentality," Nasreddine said of Vatanen's presence on the man advantage. "I know we've talked about this a lot lately, but he's one guy that truly believes it, and on the power play, you've got to shoot. It's going to create opportunities, the puck's going to get to the net, and he gets that."
Paul elected to shoot on a 2-on-1 rush, scoring with a snap shot under Blackwood's right arm to tie it 1-1 at 8:39 of the second.
"I've been trying to get one for a little bit now," Paul said of ending a 12-game scoring drought. "But it's just the way the game goes. I'm not going to think about it, just going to stay the same way. It just happened to go in tonight, which was nice."
Anisimov batted a rebound out of the air at the edge of the crease to make it 2-1 at 13:28.
Video: NJD@OTT: Anisimov cleans up own rebound in front
Gusev one-timed a pass from Vatanen from under the left face-off circle on the power play to tie it 2-2 at 15:12.
Wood took a lob stretch pass from Wayne Simmonds and scored five-hole with a snap shot to make it 3-2 at 18:00.
Chabot's slap shot from the point beat a heavily-screened Blackwood blocker side to tie it 3-3 at 15:02 of the third.
Video: NJD@OTT: Chabot hammers slap shot through traffic
"It was a weird game," Chabot said. "We tried to stay back and not give them [the least] we could. … We knew we weren't playing our best hockey game, but just the fact to bring it to overtime and tie the game, I think it was huge for us."
Senators forward Scott Sabourin, who played his first game since sustaining a facial injury on Nov. 2, had three hits in 7:17 of ice time.
"I was happy with it, baby steps," Sabourin said. "Not a ton of minutes, but that's my job. I was happy with the way my body responded with the head and everything, and I thought, considering I was out for two months, I had all the energy I needed out there. Happy to be back to playing hockey."
Video: Hughes wins it in overtime for the Devils
They said it
"That was big for us. We could've let that slide pretty easily. Two could've turned into three fast. So, it was nice for us to kind of shut them down and get the lead back. Obviously, we gave that one up [in the third], but that was good resiliency out of us tonight." -- Devils forward Jack Hughes on his team's answer to the Senators scoring two goals in 4:49 in the second period to take a 2-1 lead
"I think we were a little bit sluggish, mentally, more than legs. Conditioning wise, I think we're in good shape. We skate really well; usually we play better on the back-to-back. I would think that we'll be sharper tomorrow [against the Pittsburgh Penguins]." -- Senators coach D.J. Smith
Need to know
Hischier had a game-high five shots. … Senators forward Anthony Duclair, who had an assist, has 16 points (11 goals, five assists) in his past 12 games. … Ottawa is 9-1-2 in its past 12 home games.
Devils: Host the Boston Bruins on Tuesday (1 p.m. ET; SN, TVAS, NESN, MSG, NHL.TV)
Senators: At the Pittsburgh Penguins on Monday (7 p.m. ET; NHLN, ATTSN-PT, TSN5, RDS NHL.TV)
Video: Hughes buries OT winner as Devils top Senators