DeBrincat and Tim Stutzle scored second-period goals for the Senators (15-16-3) while Cam Talbot made 49 saves including 26 in the third period alone.
''It was an exciting game. Probably gave them a few too many looks but Talbs kept us in the game for the most part and it's nice to get the win,'' said DeBrincat. ''It's always fun to go in the shootout. Didn't really know what I was going to do, I just winged it and it worked out. It's nice to see the puck go in the net.''
Jake DeBrusk and Pavel Zacha scored in regulation for the Bruins with Zacha's goal coming at 16:27 of the third period to tie the game 2-2. Jeremy Swayman made 30 saves for the Bruins (27-4-3).
''Hats off to Talbot. That was a fun goalie battle,'' Swayman said.
The Senators had a 2-1 lead after two periods and a 21-20 shot advantage. The Bruins outshot the Senators 27-5 in the third.
''Our goal was to get better every period. I thought our first was OK, our second wasn't as good. I give credit to Ottawa, but I thought our third, we really got to our game,'' Bruins coach Jim Montgomery said.
''Talbot was incredible.''
The teams played through a scoreless first period despite a pair of breakaways by Senators forwards Brady Tkachuk and Stutzle.
In the second period, Patrice Bergeron appeared to give the Bruins a 1-0 lead, but a video review determined the play was offside and the game remained scoreless.
Stutzle beat Swayman from the right faceoff dot at 8:11 on the power play.
''I think we worked really hard, but without (Talbot) I don't think it would have been possible. He kept us in the game the whole time. They had a lot of chances, but he was there when he had to be,'' Stutzle said.
The Bruins got that goal back just over two minutes later as DeBrusk's first shot was wide but hit the end boards and bounced back onto his stick as he was about to circle the net. He had an empty net to deposit the puck as Talbot was moving the other way expecting the puck to come out the other side.
DeBrincat restored the lead for the Senators as he caught up to the puck at the top of the crease and delivered a chip shot over the shoulder of Swayman at 13:37 for a 2-1 lead.
Senators forward Drake Batherson assisted on both second-period goals and increased his point streak to 11 games. It's the highest such streak since Jason Spezza had an 11-game streak in 2011-12.
Tuesday was the second meeting of the season between the two teams. Ottawa scored a 7-5 win on home ice over Boston on Oct. 18. . Before Tuesday's game the Senators recalled defenseman Dillon Heatherington and forward Jacob Lucchini from Belleville of the American Hockey League. . Brad Marchant played his 900th career NHL game Tuesday, all with the Bruins.
Bruins: At New Jersey on Wednesday night.
Senators: At Washington on Thursday night.
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