The Red Wings are hanging by a piece of leftover tinsel, trying to claw their way into a playoff race that might be leaving them in the rearview mirror. It’s a tough situation because the Red Wings could clearly benefit from some high draft picks, but Motor City has a lot of pride in their playoff streak.

However, injuries are dealing their playoff prayers a blow. Thomas Vanek was injured in Sunday’s overtime loss to the Rangers. He won’t travel with the team to Boston for Tuesday’s contest. That’s a big game since the Bruins are in a playoff position in the Atlantic.

There’s no word on how long Vanek will be out, but he’ll miss at least one game. He’s posted 12 goals and 31 points in 35 games this season.

Photo: Kim Klement-USA TODAY Sports

They’re also moving forward without the services of Dylan Larkin. Even with his struggles this year, the loss of Larkin is big. He’s been ruled out of the next two games nursing a lower-body injury. It’s not clear if he’ll miss time after that back-to-back, but the Wings have just two games before the All-Star break. Larkin will get a little extra rest before the Wings start a crucial run of games on Jan. 31.

Additionally, defenseman Drew Miller, who was waived on Sunday, has cleared waivers.

Detroit is four points back from Boston, who holds the third playoff spot in the Atlantic. They’re also four points back from the Flyers, who hold the second wild-card berth in the Eastern Conference.

Zack Smith Extended

The Ottawa Senators signed Zack Smith to a four-year contract extension Monday. The team announced that the deal carries an AAV of $3.25 million and an actual value of $3.25 million in each of those four seasons.

Moreover, ESPN’s Pierre LeBrun reports that the contract comes with a limited no-trade clause.

The 28-year-old has 11 goals and 22 points through 43 games this season. That’s coming on the back of a stellar campaign last year where he set career-high marks with 21 goals, 36 points, four power-play goals and five shorthanded goals.

Including last season’s 20.7 shooting percentage, Smith is a 10.5 percent shooter who doubled that last year and is rolling with a 12.8 percent rate this season. He would have been an unrestricted free agent at the end of the season.

Galchenyuk Out Again

Montreal’s Alex Galchenyuk is going to miss some time, again. He’ll sit out for one game after reaggravating a knee injury that kept him off the ice for 18 games earlier in the season.

He’ll sit out of Tuesday’s game against the Flames, but it’s not clear if he’ll miss more time than that. He’s officially being designated as “day-to-day.” Montreal has just one more game after Tuesday before the All-Star break.

Kevin Hayes Out

The Rangers will be without forward Kevin Hayes for two-to-three weeks, the team announced Monday.

Hayes was injured against the Wings on Sunday. Following an MRI, it was determined he’s going to have to take a seat. The good news for the Rangers is that his time away will fall over the All-Star break, minimizing the number of games he’ll actually miss.

Logan Stanley Likely Done For Season

The OHL’s Windsor Spitfires have announced that defenseman Logan Stanley will miss four months of play following surgery to repair a torn meniscus in his right knee. The Winnipeg Jets prospect suffered the injury in a Jan. 17 game against the Kitchener Rangers.

“We’re obviously going to miss Stan on the back-end,” said general manager Warren Rychel. “He plays a ton of minutes in key situations. Other guys are going to have to step up back there while he’s out.” Selected 18th overall in 2016 draft, Stanley has put up four goals and 17 points through 35 games for the Spitfires.

The team also announced that center Logan Brown is out four weeks following a hand injury Saturday and left wing Jeremiah Addison is going to miss two weeks recovering from a bruised lung suffered when he was hit by a Sean Day slapshot.

With a record of 29-9-5-2, the Spitfires are second in the West Division and fourth in the Western Conference. This is a tough run of injuries to weather for the team, especially with it looking like Stanley is going to be done for the remainder of the season.

Odds & Ends

– With a game-winning goal in Sunday’s game against the Wild, Filip Forsberg has put up four game-winning goals in the last six games and has five in the month of January. That’s a franchise record for a calendar month. The previous record holder? Martin Erat, who Nashville traded to Washington to acquire Forsberg.

– Jake Allen has been struggling lately and the Blues gave him some time off to recollect himself. He’ll be back in the net on Thursday against Minnesota.

– Radek Faksa will miss the next two games for the Stars with a lower-body injury. Tyler Seguin could miss Tuesday’s game against the Wild with the flu.

– The Wild have reassigned winger Kurtis Gabriel to the AHL’s Iowa Wild. It’s possible they could recall one forward from Iowa before heading to Dallas for Tuesday’s game.