Jack Eichel scored twice Tuesday and has 12 goals in 26 games this season. (Getty Images)

NASHVILLE, Tenn. – When the NHL went to three-on-three overtime, it had nights like Tuesday in mind.

Jack Eichel got the puck in his own zone with plenty of open ice in front of him. He sped past Nashville’s James Neal at the red line. He cut toward the slot to leave Colin Wilson in his ice shavings. He had room to fire into the top corner before P.K. Subban could hit him.

It added up to a thrilling comeback victory for the Sabres.

“That overtime goal shows off exactly what he has in his toolbox and what kind of player he is,” Buffalo coach Dan Bylsma said after the 5-4 overtime win. “That’s a great player scoring a great goal, a highlight-reel goal on a great shot.”

On a night that started poorly for Eichel and the Sabres, all the mistakes were forgotten. In their place was a third straight overtime victory, good for Buffalo’s first winning streak since Nov. 1.

“We got down two goals on the road against a really good hockey team, and we were able to find a way to get it to overtime and win it,” Eichel said in Bridgestone Arena. “It says a lot about the resiliency of this team. It’s nice to be part of games like that.”

Eichel smiled and added, “I think we need to start winning some in regulation, though, to make it a little bit easier on ourselves.”

But that would deprive fans of the overtime magic – and the overtime magic is what made Tuesday more fun for Buffalo.

“They backed off a bit, just giving me a little bit of space,” Eichel said. “I was just trying to build some speed and attack them. I noticed that I had a forward playing D back there" in Wilson. "I just tried to use my speed and go after him, and obviously try and get a shot on.

“He’s a really athletic goaltender,” Eichel said of Juuse Saros, “and he makes it hard on you. I tried to move him a little bit and get it up, and it was nice to have that one go in.”

Eichel’s second goal of the night and 12th in 26 games wouldn’t have been possible without another comeback. The Sabres were in a 4-2 hole with six minutes to go, but Brian Gionta pulled them within a goal with 5:50 left.

“We kept playing, and we believed it was going to happen,” goaltender Robin Lehner said. “When we scored, 4-3, I had a great feeling in my body.”

The feeling spread throughout the team.

“Our guys on the bench were saying it,” Bylsma said. “We thought we could come back and win the game, even when we got down by two. Jack was saying, ‘We’re going to win this game. We’re going to win this game.’

“They go out and they do it.”

Kyle Okposo tied it, 4-4, with 1:05 to go as the Sabres pulled Lehner for an extra attacker.

“We stuck with it for 60, and that’s kind of been the motto for this team,” Eichel said. “You can see it in the last few that we’ve played. We’ve battled back and been able to squeeze out two points. At the end of the day, that’s what matters.”

With their parents waiting outside the dressing room, the Sabres walked to the team bus with smiles, jokes and embraces. They flew to Dallas for Thursday’s meeting with the Stars thinking overtime wins are fun and rallies are always possible.

“It wasn’t a pretty effort in a lot of ways, and it wasn’t the way we want to do it,” Bylsma said, “but I’ve got to give our guys a lot of kudos for keep playing and keep coming.”

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