Michael Cammalleri scored with 10.1 seconds left in regulation to tie the game at 2-2, beating Craig Anderson with a one-timer from the lower right circle with Alex Auld pulled for an extra attacker. But Kuba won it 76 seconds into OT when his wrister from center point sailed through traffic in front and went past Auld.
"It's definitely a great feeling to get two points in overtime," said Butler, who gave the Senators a 2-1 lead by scoring his ninth of the season with 2:49 left in regulation. "It was a great game, a lot of excitement in the stands, which is awesome, and it just feels great to get the win."
Anderson made 26 saves for Ottawa, which moved up to 13th in the Eastern Conference with 74 points. The Senators had made the playoffs in 12 of the 13 previous seasons, including 11 in a row from 1997-2008.
"The fans have been great," said Jason Spezza, who had a goal and an assist. "We've been out of it here for a little bit and they've kept showing up and giving great support, and it hasn't gone unnoticed in the dressing room. We've wanted to play hard to show them that we're a better team than our record is and we're going to be better next year."
Brian Gionta scored his team-leading 27th goal for Montreal, which fell short in its first attempt to give coach Jacques Martin his 600th career win. The Canadiens clinched their fourth straight trip to the playoffs with a 2-1 overtime win over Chicago on Tuesday night. They have 92 points, two more than seventh-place Buffalo, entering Saturday's season finale.
"I think that we've been playing very well lately and we had a real playoff game against the Blackhawks on Tuesday and last Saturday in New Jersey," Martin said. "Tonight we weren't as good and we didn't win so you hope to learn from those experiences."
Auld stopped 29 shots in his first game of the season against his former team.
"It's a challenge, obviously, clinching the other night and then playing against a team that's not in playoff mode," Auld said. "They're a little freer, a little looser, playing for jobs for next year."
Butler assisted on Spezza's tying goal 36 seconds into the third. Spezza got his fourth goal in three games when he put away a rebound. He drew an assist for his eighth point in three games when Butler snapped a wrist shot past Auld to give Ottawa its first lead.
Senators defenseman Francis Lessard got a major penalty and a game misconduct for his hit from behind on Montreal's Tom Pyatt 2:32 into the third. But a shorthanded chance by Ottawa's Brian Lee was the best scoring opportunity on the ensuing five-minute power play. The Canadiens were held without a shot until Anderson stopped Paul Mara's drive from the point with 1 second left in the major.
Canadiens defenseman Jaroslav Spacek returned after missing 23 games because of a knee injury that required surgery.
Gionta scored 13:13 into the second when he put James Wisniewski's rebound into an open left side before Anderson could lunge across.
"We need to be a little sharper and a little more assertive in our game. To tie it up at the end was nice, but it was maybe a bit of a mental let down after last game," Cammalleri said. "We could've done a better job of that.
"Now we have the Leafs on Saturday, and it's not very much fun playing games when you don't play your best. I'm sure we'll look forward to really getting it together, picking up the pace and prepping for the playoffs."
Material from team media and wire services was used in this report