NEW YORK — An inch or two to the right on his shot toward the empty net from three-quarters length of the ice and Mika Zibanejad would have had a hat trick.

“I thought it was going to turn,” the New York Rangers center said. “I misread that putt.”

It was about the only thing that didn’t break right for the Rangers in a season-opening 3-1 win against the Tampa Bay Lightning at Madison Square Garden on Tuesday, a victory that validates the feeling their players, coaches, management staff and fans had about the type of team they can be this season.

“I hope we play like this most nights,” coach Gerard Gallant said. “This is what I see. This is what I believed in our team. This is what I expect from our group, it really is.”

Zibanejad led the way offensively with a short-handed goal at 3:25 of the second period to give New York a 1-0 lead and a power-play goal at 5:11 of the third period to make it 2-1. He finished with nine shots on goal and went 9-for-13 on face-offs in 23:13 of ice time.

“He was outstanding,” Gallant said. “The line played great, the team played great, but he was definitely the leader.”

Igor Shesterkin did his job too in a rematch of last season’s Eastern Conference Final, outdueling Andrei Vasilevskiy by making 25 saves, including all 10 shots he faced in the third.

But this was more than a night for just Zibanejad and Shesterkin. This was a night for the Rangers as a team, the kind of night they didn’t have on a consistent basis until late in the second half of last season because of defensive deficiencies and turnover issues.

“I didn’t think we shot ourselves in the foot at all,” defenseman Jacob Trouba said following his first game as a captain of an NHL team. “When plays were there to be made, we made them, but when there wasn’t a play, I don’t think we turned too many pucks over in bad areas. ‘Shesty’ was good. Everybody just played a solid game. I thought we played well in front of him.”

Too often last season they didn’t, only to watch Shesterkin bail them out time and time again.

That didn’t happen Tuesday.

New York kept Tampa Bay to the outside at 5-on-5, limiting it to 18 shots at even strength. The Rangers also blocked 12 shots.

They didn’t let the Lightning get much closer when they were on the power play, allowing only a 5-on-3 goal from Steven Stamkos on a one-timer three seconds after a face-off win by Brayden Point.

Tampa Bay’s power play went 1-for-6 with eight shots on goal and a short-handed goal against. New York will take that every night, although fewer penalties would help too.

“If you watched us last year at this time, we were pretty loose in the defensive zone, so I thought we did a real good job there,” Gallant said. “That’s the biggest thing. That’s really where it starts.”

New York’s power play was dangerous, going 1-for-4 with 14 shots and long stretches of offensive-zone possession time.

Chris Kreider had a potential power-play goal from along the goal line early in the second period stuffed by Lightning defenseman Mikhail Sergachev, who made a terrific play with his stick before Vasilevskiy got across the crease to make a save with his right pad.

Vasilevskiy also came across with his right pad to rob Kreider of a power-play goal from the goal line late in the first period.

“It’s one game, but obviously the way we played tonight, we played a lot like we’ve been talking about and how we talked about last year,” Zibanejad said. “I don’t think we over the summer changed the way we want to play. We know what we have to do, and it’s trust ourselves, trust the system and trust the players, everyone in here. I thought we did a good job, and we have to keep doing that.”

The Rangers didn’t want to make a big deal of the win, especially because they leave after practice Wednesday for back-to-back road games in home openers for the Minnesota Wild on Thursday and Winnipeg Jets on Friday.

“We’ll see what we do on this road trip, and then we’ll see how the start goes,” Trouba said.

They also tried not to make it a big deal that they played this well against the Lightning, the three-time defending conference champions who eliminated them from the playoffs last season by winning four straight after losing Games 1 and 2.

“I think it’s more from you guys to try to create a story for this game,” Zibanejad said.

Except that’s not entirely true, because Zibanejad later said that what happened against the Lightning in the conference final last season is motivation for the Rangers.

He said they saw what it takes to win in June and the hope is they’re better for it in October, so they have a chance to get back to playing hockey in June next year.

So far so good.

“It’s definitely better standing here after Game 1 and having a win and to play like that than to be worried about a lot of things,” Zibanejad said.