Carey Price made 26 saves for his fourth win in as many starts. He has allowed four goals on 112 shots over that span.
WATCH: All Canadiens vs. Rangers highlights
Montreal finished 3-0-0 against New York (41-22-2) this season.
"There's been a lot of talk of us probably matching in the first round [of the Stanley Cup Playoffs], so we wanted to come in here and play a strong game," Montreal center Alex Galchenyuk said. "We did."
The Canadiens had 35 shots on goal, the most they've had under Julien.
"We talked about it this week where defensively we got a little bit better, and now it was a matter of maybe better execution, managing the puck a little bit better and creating a little more offense," Julien said. "I thought we moved the puck fairly well tonight. We threw more pucks at the net than we have in a while and we had a nose for it. We really wanted to get pucks in deep and get our forecheck going, which I think is a strength of this group."
New York lost its fourth straight game at home (0-3-1). Henrik Lundqvist made 31 saves and Chris Kreider scored his 24th goal of the season. The Rangers play their next four games on the road.
"We were slow all over the ice, getting beat to pucks and letting them have all the plays they wanted," Rangers captain Ryan McDonagh said. "It was an easy game for them."
Shaw's goal, his 10th, put the Canadiens up 3-0 at 18:37 of the second period after Lundqvist lost sight of the puck as it went behind the net. Shaw scored on a wraparound.