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NEW YORK -- Mika Zibanejad wasn't sure he'd be saying it after the third game of the season.

But he did, and it's telling for how the New York Rangers have started their first season under coach Peter Laviolette.

"We're starting to get it," the center said following a 2-1 win against the Arizona Coyotes at Madison Square Garden on Monday. "We have things to work on like every team does, but it's a lot easier when the things we want to be good at are clicking right now, not to the fullest but definitely heading toward the right direction."

That the Rangers are this early in the season, with two wins in their first three games, is significant because so much of what Laviolette is coaching them to do is new for them, and finding ways to win while they adjust will pay off in a big way down the road.

New York has played three different types of games, from near-flawless structured against the Buffalo Sabres to more open game against the Columbus Blue Jackets to the grind-it-out battle against Arizona in its home opener.

The 'NHL Now' crew talks Rangers win in home opener

The Rangers felt good about all of them, even the 5-3 loss they had in Columbus on Saturday, when they doubled up the Blue Jackets in shots on goal (42-21) and were one shot attempt away from doing it in that statistical category too (93-47).

They lost, but it wasn't because they were outplayed.

"They kept showing advanced analytics on the jumbotron and it felt like we were leading in every category," forward Vincent Trocheck said. "Considering new systems and everything and only having training camp and a couple games to get into everything, figure out all the systems, I think we're playing great. Most importantly, our defensive game has been so solid."

He's right about that, especially with the newness of the systems.

The Rangers defend with a hybrid system between man-to-man and zone after playing mostly zone the past two seasons under former coach Gerard Gallant. They get into a 1-3-1 structure in the neutral zone and try to push the attacking team to the right side.

In fact, on Monday they were so good at it at times that the home fans started booing the Coyotes because they would basically stop and hold the puck at their own blue line for a few seconds, trying to process how to best navigate through the narrowest of openings the Rangers were giving them in the middle of the ice.

"Yeah, it's frustrating to play against," Trocheck said. "I mean I've played against Pete's teams in this league for a long time, and it's really frustrating when you're a guy that likes to take the puck through the neutral zone with speed. It's tight in there."

There's also less chasing behind the net, more creating off turnovers, the ability to attack but stay patient, and pressure all over the ice.

"A team that can limit teams to a two- or one-goal game, it makes you so confident that you're going to win more games," Trocheck said. "If we're playing as good as defense as we are and you have 'Shesty' (goalie Igor Shesterkin) back there, it makes it so much easier on the mind. And we know with the offensive skill in here we're going to score goals and that's going to lead to a lot of wins. I'm not really worried about us putting the puck in the net."

The Rangers have 10 goals in three games, including a 5-1 win against the Sabres in the season opener last Thursday. It was the defense, specifically the penalty kill and Shesterkin, that led to the win against Arizona.

New York killed a two-minute 5-on-3 that started with 1:19 remaining in the second period. They allowed two shots on goal and blocked two shots.

"I thought we got some momentum out of that and came up with our own power-play goal," Zibanejad said.

They did on Trocheck's deflection goal that made it 2-1 at 8:26 of the third.

Shesterkin came up with a penalty-shot save on Jason Zucker with 4:48 remaining. It was really one of the few times after Trocheck's goal that the Coyotes got some pressure on the Rangers. They weren't content to play prevent defense with a one-goal lead.

"We started to press and own the offensive zone more and more," Laviolette said.

It was another positive sign in a series of them through the first 180 minutes of the Rangers season, which so far looks like a 180-degree difference from the team that finished last season under Gallant.

"It is getting better and better," Laviolette said. "From where we were in game three of the exhibition season, or when we were bumping into each other in practice trying to figure out how we're going to move as a group, I do see more continuity and more fluidness to our game. But there's still things there and we'll just continue to teach. The players, they're on board, they're trying to understand and get it."

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