DETROIT -- Athletes are taught to maintain a narrow focus and live for today but Saturday, the Detroit Red Wings and Montreal Canadiens couldn't help but look ahead.

After Atlantic Division champion Montreal recorded a 3-2 overtime decision over Detroit, the thoughts of the Montreal players, who'd completed their regular season, turned to the New York Rangers, their opponents in the first round of the Stanley Cup playoffs.

"Obviously we're happy with the season we've had and I think when you wake up tomorrow, the preparation for New York is going to start," Montreal forward Brendan Gallagher said. "It's going to be a fun series I think."

For the Red Wings, who will miss the playoffs for the first time since the 1989-90 season, thoughts turned to saying goodbye to an old friend. Sunday, they face the New Jersey Devils in the farewell game at the Joe Louis Arena, the team's home since 1979 which will be mothballed in favor of brand new Little Caesars Arena.

"Tomorrow is a big day," Detroit captain Henrik Zetterberg said. "It's a big day for everyone."

The Canadiens improved to 47-26-9 when Alex Galchenyuk drove a shot through the legs of Detroit goalie Petr Mrazek 1:42 into the overtime period.

"That was an amazing feeling," Galchenyuk said. "The crowd was so emotional because of what is happening with this building, so it was a great goal to get.

"I wish I had kept the puck, because it was a great way to finish our last game here and to end the season."

Artturi Lehkonen and Nathan Beaulieu also scored for Montreal, and Nesterov notched two assists.

Frans Nielsen and Dylan Larkin each scored for Detroit.

On the winner, Wings defenseman Mike Green lost control of the puck in the Detroit zone. Nesterov pounced on the turnover and fed Galchenyuk for his one timer.

"It happens, it's three-on-three," said Mrazek, who stopped 27 shots. "The turnovers happen there. It's a big disappointment for me, obviously, in my last game at the Joe I wanted to win."

Jimmy Howard will get the start in goal for Detroit (32-36-13) in Sunday's season finale.

Montreal goalie Charlie Lindgren made 25 saves to improve to 3-0 as an NHLer.

"It's awesome," Lindgren said. "It's really a blast. It's been a good start to my National Hockey League career.

"Again, though, I thought the guys played great. We got some huge blocks tonight, especially in crunch time."

Even with Montreal sitting out several regulars and while a boisterous crowd cheered their every move, the Red Wings struggled to get their game into gear.

"It was a playoff atmosphere," Detroit forward Dylan Larkin said. "They were into it and they deserved to be. We're trying our best for them and they're paying a lot of money to come see us play in this building.

"I wish we came out a little bit harder. I look at myself and look in the mirror, and hopefully we're going to come out hard and play hard for them tomorrow."

Nielsen opened the scoring 10:44 into the first period after a clearing attempt by Canadiens forward Andreas Martinsen bounced off a stanchion right to Red Wings forward Darren Helm. Helm passed to Nielsen, who tucked a high backhander past Lindgren.

The Canadiens drew even on the power play 4:19 into the second period when Beaulieu's point shot through traffic slipped between Mrazek's arm and body.

Larkin put the Red Wings back in front when he one-timed Tomas Tatar's feed past a sprawling Lindgren at 12:51 of the second frame.

Montreal forged a tie with 1:30 left in the session as Mrazek stopped Nesterov's point blast, but Lehkonen shoveled home the rebound.

NOTES: F Steve Ott, who was traded to the Canadiens by the Red Wings last month, played his first game in Detroit since the deal. ... The Canadiens sat out several of their regulars, including G Carey Price, D Andrei Markov and Fs Alexander Radulov, Tomas Plekanec and Max Pacioretty, who were rested. Ds Shea Weber (lower body), Jordie Benn (upper body), Alexei Emelin (lower body) sat because of injury. ... The Canadiens recalled D Mikhail Sergachev, their 2016 top draft pick, from Windsor of the Ontario Hockey League on an emergency basis. ... F Matt Lorito made his NHL debut for the Red Wings and picked up an assist. ... The Red Wings went 19-14-5-1 against the Canadiens at Joe Louis Arena. ... Red Wings F Dylan Larkin will play for Team USA in the world championship.