Phaneuf scored on a slap shot from the point 12 seconds after a third-period delay of game penalty to Bruins defenseman Zdeno Chara expired.
"We didn't draw it up like that, for sure, but playoffs, it's about momentum, sticking to it, continuing to find a way to push your game," Phaneuf said.
"That's the biggest one I've scored. It feels great to do it here, in front of our fans. Just incredible. I've played a long time (12 seasons) and it's my first (playoff) overtime winner. It feels great."
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Clarke MacArthur scored his first goal in almost two years, Chris Wideman and Derick Brassard scored, and Craig Anderson made 26 saves for the Senators, who trailed 3-1 in the third period.
Drew Stafford, Tim Schaller and Patrice Bergeron scored for the Bruins, and Tuukka Rask made 25 saves.
The Senators tied the game on goals by Wideman at 5:28 and Brassard at 7:48.
"Fairly typical," Bruins coach Bruce Cassidy said. "A team that's behind, they're at home, they're desperate, they're going to push hard and they did. We saw the same script on Wednesday (winning Game 1 2-1 after trailing 1-0). We did it to them. What's disappointing is we're generally are pretty good at closing out games."