Nobody said it outright in the lead up to the first of a back-to-back, home-and-home matchup with the Penguins on Saturday, but winning this set of games — or at least avoiding a sweep — was as essential a task as the Islanders have faced all season.

For weeks now, the Islanders have hung around on the periphery of the playoff race, too far back to really be a factor, but close enough that a three-game winning streak could in theory vault them above the cutline.

If they’d lost both games to the Penguins, though — and after a 7-1 embarrassment against the Sabres heading into the holiday break?

Well, Pittsburgh came into Saturday four points ahead of the Islanders and a point behind Ottawa, which occupied the last playoff spot.

You can do the math on how it would have looked had the Islanders lost a pair of four-point games.

Instead of staring down that reality, a 6-3 win over the Penguins at UBS Arena on Saturday, combined with a Senators loss to the Jets, means that — at least for 24 hours — the Islanders are a mere three points off the playoff cutline.

“No one was happy to be embarrassed in front of our fans,” coach Patrick Roy said, referring to the meltdown against Buffalo five nights prior. “… I could tell today when I did the meeting before the game, I think they didn’t want to listen to me. It didn’t matter what I would say. They wanted to play that game.”

Winning did not come so easily after a 4-1 lead turned to 4-3 heading into the third after consecutive goals from Noel Acciari and Rickard Rakell, with the Islanders looking to be in real danger of blowing another game in a season full of should-have-been.

The game seemed to be trending toward fireworks in one direction or the other.

But the Islanders — who quietly have not blown a lead in exactly a month — did not cede to the habits which haunted them in October and November.

Instead, they shut the game down, keeping up the physical play they’d sustained throughout and turning the match into a low-event slog, with the visitors recording all of eight shots in the last 20 minutes.

This match could be framed as the Islanders’ formerly injured stars finally looking like themselves, with Anthony Duclair scoring and Mathew Barzal getting his first five-on-five point of the season with a beauty of a first-period assist to Jean-Gabriel Pageau.

The more accurate way to do so, however, would be in terms of the intensity and edge that has been lacking for much of the season, being very much present.

It was fitting, then, that Casey Cizikas — who has defined the team’s battle level for much of the past decade — sealed the win with a goal off the rush with 5:17 to go in regulation, his second goal of the game after being elevated to Bo Horvat’s line in place of Maxim Tsyplakov during the second period after the latter took consecutive offensive zone penalties.

For Cizikas, whose start to the year has been rough, the two goals marked a doubling of his point tally so far this season.

For the Islanders, they sealed a desperately needed result — with Anders Lee’s second goal of the evening going into the empty net to cap it off.

“That’s the biggest thing is being hard on guys,” Cizikas said on a night where the fourth line — across multiple configurations — did not allow a shot attempt while on the ice. “You don’t expect everyone to go out there and lay the body and lay that big hit, but if you’re hard on guys, you’re hard in the corners, you’re heavy on them, that takes a toll as well.

“I think that was a great job by us in a game that was physical, that was chippy, which is good hockey in my opinion. I think the refs did let a lot of that go. It went both ways. Those are games that are fun to play in. But if you’re hard on pucks, if you’re hard on bodies, I think that’s just as important as being physical and if you get a chance to maybe make a big hit, you make a big hit.”

Whether you call it physicality or prefer Cizikas’ phrasing of being hard on pucks, that has been missing from the Islanders’ game for much of the season.

It is no coincidence that it showed up in both their recent 6-3 wins, in Toronto on Dec. 21 and again on Saturday.

“We battled hard,” said Pageau, who opened the scoring on Barzal’s feed. “Every one-on-one battle, I thought we played hard.”