In the previous six matchups before Tuesday’s 3-1 win over the Sabres, the Rangers grappled with finishing games rather than getting off to strong starts.

In fact, the Blueshirts had outscored their opponents 10-3 in the opening 20 minutes, dating to the 6-3 win over the Devils on April 17. They had given up six goals, however, in third periods over that same span, allowing teams to make things interesting toward the end of games.

It was the opposite Tuesday night against the Sabres, when the Rangers were outshot 16-6 in the first period. Somehow — well, with Igor Shesterkin’s stellar play in net — the Rangers survived and escaped with the game still scoreless.

“We got better as the game went on, no doubt,” said Ryan Strome, who assisted on Alexis Lafreniere’s game-winner in the third. “I think lately our starts have been good, and we haven’t been finishing the game. [Tuesday night] was a little different. Proud of our effort. I think at this time of the year, these wins are huge, it doesn’t really matter how we get them. I thought we banded together in the third period. We had a couple good penalty kills, power play was able to get one. We found a way.”

Season-deciding games on the horizon for the final six matchups against the upper-echelon of the division — the Islanders, Capitals and Bruins — so the Rangers won’t be able to afford any lackluster periods. It will take a full 60-minute effort each night for them to have a chance of squeezing into the postseason by stealing one of the four playoff spots from either the Bruins or the Islanders.

The Rangers have averaged four goals per game in their past 10 games, which will be crucial to maintain. A scoring dip would be detrimental, considering they own a league-low .211 winning percentage in one-goal games and have just four victories under those circumstances.

“I don’t think we were too happy with our first, I thought they came on really well, they played a good first,” Brendan Smith said of the Sabres. “We knew what we had to do, we talked about it in the dressing room. I think from the second it just continued to get better. So it was kind of a trickle-down effect, just of what we had to do and get better at, kind of come through the system and it took care of us.”

“That’s kind of the whole thing we’ve been preaching, if you follow the system, it will take care of us, and that’s what happened. Ultimately, the third period became our best because we wore them down.”

The Rangers have won nine of their past 11 home games, posting a 9-2-0 record and outscoring opponents 54-25 over that span. They also have earned at least one point in 11 of their past 13 home games.

Three of the Blueshirts’ final six games of the season will be at Madison Square Garden.