NEW YORK -- After two days of learning systems and getting comfortable with the coaching change, the Montreal Canadiens put together the game coach Claude Julien was hoping to see Tuesday.
The Canadiens defeated the New York Rangers 3-2 in a shootout at Madison Square Garden, where the home team had won five consecutive games.
"It's a momentum-builder," Montreal goalie Carey Price said.
WATCH: All Canadiens vs. Rangers highlights
Paul Byron scored in the fifth round of the shootout to help the Canadiens (32-20-8) end a three-game losing streak and get their first win in two games since Julien took over for Michel Therrien last week.
Alexander Radulov also scored in the shootout, and Shea Weber and Andrew Shaw each had a goal.
Price made 28 saves, including a diving save on Rangers forward J.T. Miller with 3.7 seconds left in overtime, for his 258th victory with the Canadiens, tying Ken Dryden for third on Montreal's all-time wins list.
The Canadiens stayed in first place in the Atlantic Division, two points ahead of the Ottawa Senators, who have two games in hand.
"Playing the way we did tonight hopefully encourages us to play that way moving on here," Julien said. "It wasn't the perfect game, but our compete level was good, and when your compete level is good, you have a chance to win. I thought our guys did a great job of that."
The Rangers (38-19-2) got game-tying goals from Oscar Lindberg in the first period and Rick Nash in the second. Henrik Lundqvist made 26 saves.
Video: MTL@NYR: Shaw beats Lundqvist with a wraparound
New York is 7-1-1 in its past nine games.
"We played well enough to win it," Lundqvist said. "It came down to some extra shots in the end, but we definitely had the looks and we worked hard all over the ice. We just played a really good team. They had a strong game as well. There are a lot of good things to take with us here for next game. I am pretty disappointed right now, but I appreciate the effort from everyone."
Shaw gave Montreal a 1-0 lead at 3:55 of the first period with a wraparound goal. Lindberg tied it at 10:03 by redirecting Jesper Fast's pass to the slot past Price.
Montreal took a 2-1 lead on Weber's power-play goal at 1:42 of the second period.
Nash tied the game 2-2 with a breakaway goal at 9:26. It came 6:05 after he was denied by Price on a breakaway.
Zuccarello scored in the first round of the shootout. Radulov tied it in the second round. Price made saves on Derek Stepan, Jimmy Vesey and Miller to keep the Canadiens in it so Byron could win it.
"All the stuff we've been doing in practice, it's reinforcing everything the coach is telling us to get a win against a very good Rangers hockey team on the road," Byron said. "It can give us a lot of confidence."
Video: MTL@NYR: Nash breaks in and finishes top shelf
Goal of the game
Byron cut wide right and moved back to the middle before beating Lundqvist with a shot through the five-hole for the deciding goal.
Video: MTL@NYR: Byron beats Lundqvist five-hole for SO win
Save of the game
Price was at the top right part of the crease when Miller got the puck from Kevin Hayes in the right faceoff circle off of a 2-on-1 rush with 4.7 seconds left in overtime. Price dove across the crease with both arms up and a second later he made the save of the night to deny Miller of what looked like a sure game-winning goal.
"It was just a desperation move," Price said. "It hit me in the back of the arm, so yeah, I was pretty lucky."
Video: MTL@NYR: Price dives for remarkable late save in OT
Highlight of the game
Price's save on Miller was the end to the highlight of the game. Canadiens center Tomas Plekanec hit the post with a shot from the left circle eight seconds earlier. The rebound came out to Hayes, who started the 2-on-1 breakout with Miller against Andrei Markov. Price did the rest.
Unsung performance of the game
Pacioretty stepped into the faceoff circle to replace Phillip Danault at the start of Montreal's power play early in the second period. He won the faceoff by battling for the puck and chasing it down at the boards. He then started the quick passing sequence that led to Weber's one-timer goal.
Video: MTL@NYR: Weber unleashes big blast for PPG
They said it
"We were desperate. We need to play that way for the rest of the season if we're going to find that consistency in our game." -- Canadiens goalie Carey Price
"We knew that they were going to come and have like a desperate approach to this game. I thought we matched it. We definitely had our chances." -- Rangers goalie Henrik Lundqvist
Need to know
This was the third Rangers home game to go to overtime, first since Dec. 18. All three have ended in a shootout. It was New York's seventh overtime game, the fewest in the League.
Canadiens: Host the New York Islanders on Thursday (7:30 p.m. ET; SNE, RDS, MSG+, NHL.TV)
Rangers: At the Toronto Maple Leafs on Thursday (7:30 p.m. ET; SNO, TVA Sports, MSG, NHL.TV)
Video: Price, Byron lead Habs to 3-2 SO win