Red Wings right wing Christian Fischer scores on Islanders goaltender Ilya...

Red Wings right wing Christian Fischer scores on Islanders goaltender Ilya Sorokin as Alexander Romanov defends in the second period of an NHL game Thursday in Detroit.  Credit: AP/Paul Sancya

DETROIT — The losing streak is at six and the season is on the brink.

Sure, the Islanders still are mathematically alive. But Thursday night’s discouraging 6-3 loss to the Red Wings at Little Caesars Arena left them a cavernous five points behind the hosts for the Eastern Conference’s second wild-card spot with 13 games left.

Discouraging because, for most of the first two periods and then in the third after they fell behind by four goals, the Islanders played some of their best hockey in a long while.

“I know the name of the game is winning, but our guys played a really good game,” coach Patrick Roy said. “I would like to be negative, but there’s nothing to be negative about. Maybe a couple of turnovers. Other than this, we deserved better than what we got.”

The Islanders (29-25-15) were done in by their penchant for allowing goals in bunches and, in those crucial stretches, some of the defensive disorganization that has marked this losing streak. The Red Wings scored twice in 2:08 late in the second period to take a 3-1 lead and increased that to 5-1 with two goals within 1:10 in the third period.

“I think we vacated the lanes a few times,” defenseman Robert Bortuzzo said after logging 12:19 in his return from an ankle injury that had kept him out since Jan. 4. “If you let good players inside your house, it’s going to bite you.”

Roy altered his lines, moving Mathew Barzal back to center for a whole game for the first time this season as he skated between Anders Lee and Hudson Fasching. Jean-Gabriel Pageau centered Pierre Engvall and Simon Holmstrom and Casey Cizikas was back on the fourth line, with rookie Kyle MacLean sliding to left wing.

Ilya Sorokin made 18 saves and James Reimer stopped 33 shots for the Red Wings (36-28-6). The Islanders also dropped six points behind the Flyers for third place in the Metropolitan Division.

“It’s not from a lack of effort,” said Pageau, whose power-play goal at 9:34 of the third period coupled with Barzal’s deflected shot at 11:20 added some suspense to the final minutes. He added that there were “no quitters.”

Dylan Larkin, back in the Red Wings’ lineup after missing eight games with a lower-body injury, ended any suspense with an empty-netter at 16:15 for his second goal. Andrew Copp also scored twice for the Red Wings. His second one made it 4-1 as he got free to the crease to finish an odd-man rush at 5:12 of the third period. Patrick Kane converted another odd-man rush at 6:22 for a four-goal lead.

“It’s definitely unacceptable, for sure,” defenseman Mike Reilly said. “That’s on us to not sit back. They kept coming. You could tell they weren’t stopping at three goals. We should have been prepared for that way better.”

Reilly tied it at 1-1 at 13:25 of the second period with a shot from the left point that Reimer let trickle through his pads. Copp made it 2-1 at 16:00 of the second period.

Larkin, left wide open in the slot, then blasted in a shot for a 3-1 lead at 18:08.

So now the Islanders face an improbable playoff push.

“It is [a big hole],” Bortuzzo said. “I’m not going to sugarcoat anything this time of year. We haven’t had that jumping-off game where it’s something we can build off of. Just looking to find that, and then you can build a little mojo. Guys are wearing a little bit of confidence stuff. That comes with losing. It’s frustrating. But no one is throwing in the towel.”

Notes & quotes: Roy said Semyon Varlamov will start Saturday afternoon against the Jets at UBS Arena and Sorokin will face the visiting Devils on Sunday . . . Engvall logged 13:58 without a shot after being a healthy scratch on Tuesday. . . Defensemen Sebastian Aho and Samuel Bolduc and forwards Matt Martin and Oliver Wahlstrom were the healthy scratches.

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