DETROIT – The Wild clinched a playoff berth while many were sleeping in the wee hours of Sunday morning by virtue of the Los Angeles Kings losing.

But Sunday afternoon in the team's final visit ever to Joe Louis Arena, it still felt like the desperate-for-something-good Wild was fighting for its playoff lives.

In a tight-checking game as the Wild tried to revive some good habits and rid itself of the stench from a rough month, the Detroit Red Wings — the second-worst team in the Eastern Conference — rallied from a pair of one-goal deficits to eventually win 3-2 in overtime.

But when you are 2-9-1 in the past 12 games and 3-10-1 in March after not so long ago leading the Western Conference, sometimes you have to grasp for positives.

"That's the best game we've played in a month," coach Bruce Boudreau said a day after saying he was "embarrassed" after a loss to Vancouver. "To hold this team to under 20 shots, in their building, where they count everything that even looks like a shot, pretty good."

The Wild held the Red Wings, about to miss the playoffs for the first time in 26 years, to three third-period shots. With the Wild leading 2-1, one of those shots, 55 seconds in, sailed by Devan Dubnyk off a Tomas Tatar power-play one-timer. In the final minute of regulation, Red Wings goalie Jimmy Howard came up large on Eric Staal and Jason Zucker, then again on a 2-on-1 shot by Erik Haula in overtime.

Seconds later, Andreas Athanasiou ended things by jumping on the ice after a line change and scoring off a breakaway after faking backhand. That caused Dubnyk to guess and go for a diving poke check.

Dubnyk was dead meat once the skilled speedster suavely went to his forehand.

The Wild's past four losses and five of its past six are against non-playoff teams.

But, captain Mikko Koivu said, "I thought it was better. That's not enough. But you've got to start somewhere. There was a lot of good in that game, and we just came short."

Staal gave the Wild a 1-0 lead with his team-leading 26th goal in the first period, but a strong period was destroyed when Mike Green one-timed the tying goal with 18.5 seconds left. Charlie Coyle iced the puck, then taking the faceoff on his strongside in the right circle, he lost it clean and Dubnyk allowed a screened goal.

But late in the second, defenseman Nate Prosser scored his first goal in more than two years after Staal forced a turnover and Prosser's shot deflected off Dylan Larkin's stick.

It was Prosser's first goal since Feb. 14, 2015, ending the second-longest goal drought in the NHL at 106 games (Brian Dumoulin, 146 games), according to the Elias Sports Bureau. It actually had been 183 Wild games since the oft-scratched defenseman scored.

Prosser had himself a fine game. He saved a potential goal in the first period, and in the second with the score tied, he covered up for partner Jonas Brodin fanning on a one-timer by reading the play, catching up to Athanasiou on a breakaway and muscling him off the puck.

But mostly, Prosser said, "It feels good to score again. It's been a long time."

The moral victory story line might be hard to digest, and there's no doubt the Wild's long list of snakebit players again failed to deliver when needed.

But with the Wild frantically trying to patch its game together, players and Boudreau seized the good things from Sunday with powerhouse Washington arriving in St. Paul on Tuesday.

"We played the right way today," Boudreau said. "We got it deep when we had to get it deep, you didn't see the constant odd-man rushes against for the most part. You saw playing the smart way, and I thought we had good chances to score and win the game."

Added Staal, "We're after wins here and two points every night."

But after chasing games and not engaging way too often lately, Staal said, "Our battle level was high. Our compete and hunger to get back on the track that we want to be on was a lot better."