BUFFALO — The teachings of Peter Laviolette’s first training camp with the Rangers resonated enough for the team to translate it to the ice in the first game of the season.

It was evident that the Blueshirts had spent the last three weeks following a new voice.

One that had the club playing a much more structured style that led to a commanding 5-1 win over the Sabres on Thursday night at KeyBank Center.

After enduring a slate of exhibition games that were naturally filled with disarray, the Rangers looked like a team that had absorbed every pointer it was given in the preseason and applied it the instant it actually mattered.

Perhaps the anticipated learning curve won’t be as arched as originally thought.

“I think every day of camp we got better and better at the systems and Lavi’s message was just to outwork them and what we’ve done with our systems should take care of itself,” Nick Bonino told The Post after the game.

The Rangers had already built themselves a 3-0 lead just over halfway through the second period, but the defense up until that point was just as notable as the score.

Not only did the Rangers tilt the ice on offense, outshooting the Sabres 31-25 overall, but they looked vastly different in the neutral zone than they have in years past.

They anticipated passes and were simply in better position to limit offensive-zone entries, in addition to showing a clear plan for how they wanted to push the puck up the ice.

“That’s one of the hardest things to get a grip on, is the neutral zone, because it’s foreign to a lot of guys,” Bonino said. “It’s good that we made mistakes in preseason because they’re easy to fix. Once you get that down, it does limit their rushes, it does limit what they can do with the puck.”

Buffalo struggled to generate high-quality scoring opportunities through the first two periods in particular, while the Rangers doubled the home team’s high-danger chances, 6-3, over the same span, according to Natural Stat Trick.

The Sabres couldn’t get one past a sharp Igor Shesterkin until the 18:30 mark of the middle frame, when JJ Peterka followed up on a blocked shot and cut the Rangers’ lead to two.

After fighting off a 12-second five-on-three disadvantage later in the third period, Mika Zibanejad’s individual effort at the other end allowed the Rangers’ No. 1 center to dish to a streaking Chris Kreider for the shorthanded goal — his second of the night after a power-play tally in the first — and the 4-1 lead.

Jacob Trouba’s empty-net goal shortly thereafter sent Buffalo fans for the exits.

There haven’t been too many instances in recent years when the Rangers finished games just as effectively as they started them, or vice versa.

It was usually one or the other, but the 60-minute effort was there Thursday night.

“There’s a lot that went into training camp, they put a lot into it,” Laviolette said. “It’s one game, but there were positives to pull from that. The guys played hard.”

The first game of Laviolette’s Rangers tenure couldn’t have gone any better unless the new head coach had drawn it up himself.

From puck drop, his newly constructed second line of Artemi Panarin, Filip Chytil and Alexis Lafreniere was buzzing.

As a unit, they combined for two goals, including Panarin’s bullet from the slot for the 3-0 edge in the second.

And the first goal of the Rangers’ season belonged to none other than Lafreniere, who put forth arguably one of his best games of his young career after drawing heaps of negative attention in the preseason.

It wasn’t just Lafreniere who struggled in the preseason, either.

The Rangers as a whole had some concerning moments.

Those games, however, didn’t count.

This one did.