The Rangers were lucky to escape the first period Tuesday night without letting Buffalo score, after allowing the Sabres to have their way in the offensive zone and pour on the shots as if they were the ones fighting for a playoff berth.

Defenseman Brendan Smith opened the scoring early in the second period for the Rangers, but Sabres center Sam Reinhart’s power-play goal tied it up with a mere 4 seconds left in the middle frame.

So with the game on the line in the third period, the Blueshirts had to fend off another heavy power play from the Sabres. That prompted head coach David Quinn to inform Alexis Lafreniere that he would be taking the next shift on the second line with Ryan Strome and Artemi Panarin to get fresh legs on the ice.

Moments before hopping over the boards for that shift, which culminated in the Rangers rookie scoring the game-winning goal, Lafreniere turned to Strome and asserted his confidence that has lately enraptured the rest of the team.

“[Lafreniere] actually said before we went on for that shift, ‘We’re going to go get one,’ ” Strome said after the 3-1 win Tuesday.

The 2020 first-overall pick followed through on his words, taking a pinpoint pass from Strome and ripping a bullet shot from his knees past Sabres netminder Ukko-Pekka Luukkonen to give the Rangers a 2-1 lead.

It was Lafreniere’s 10th goal of the season, which lifted him to seventh among rookies in the NHL in goals. He is also now in a three-way tie, with the Predators’ Eeli Tolvanen and the Lightning’s Ross Colton, for the most game-winning goals among rookies with four.

Since switching places with Chris Kreider on the top line next to Mika Zibanejad and Pavel Buchnevich for the 3-2 loss to the Flyers on April 22, Lafreniere only went that game without a point. In the past three contests, the 19-year-old has two goals and two assists.

“I know people were making a big deal of what his stats were earlier in the year, but he just played in his 50th game,” Quinn said Tuesday. “In a normal season, he would’ve had 32 more games to go, playing the way he is, playing on the line he is. He’s having a really good rookie year. With no training camp, with no exhibition games, it’s hard for these young players to get acclimated to the National Hockey League. If he had a three-week training camp with six exhibition games, the beginning of the season may have been a little bit different. But I think it speaks to his commitment, to his coach-ability, to his love for the game.

“That’s the thing that really jumps out at you when you coach him, how much he loves hockey. What an infectious personality he has on top of all the talent that he has.”

Infectious is the word that several of Lafreniere’s teammates have used to describe him. It’s easy to see even watching practice through a live stream. The Canadian teen talks to everybody, is incredibly affectionate and is never not smiling.

Lafreniere has been said to “light up a room” since he joined the team, but it’s been the evolution of his confidence that has beguiled the Rangers.

“I think I’ve always been the same, I’m just happy when guys have good games, when they make great plays,” Lafreniere said earlier this week. “Just happy to be here for sure. And with the group we have, it’s always a lot of fun.”