DETROIT -- The Detroit Red Wings held on to bolster their playoff chances.

Riley Sheahan scored two goals, and Detroit edged the Montreal Canadiens 4-3 Thursday night at Joe Louis Arena.

The Red Wings led 4-0 early in the second period.

"They found a way how to come back to the game, but in the end it doesn't matter," said Detroit goaltender Petr Mrazek, who made 26 saves. "You got two points, and nobody's going to ask you in a couple days how you won the game."

Detroit, which has made the Stanley Cup playoffs in each of the past 24 seasons, is one point behind the Boston Bruins for third place in the Atlantic Division with a game in hand. The Red Wings also are tied with the Flyers for the second wild-card position, though Philadelphia has a game in hand.

Luke Glendening also scored and Anthony Mantha got his first career goal for Detroit. Mike Green and Brendan Smith each had two assists.

"We got to win hockey games, period," Detroit coach Jeff Blashill said. "There'll be lots of other tough games for other teams, but we have to win hockey games. We have to earn our way in, and to do that, you've got to win."

Tomas Plekanec, Paul Byron and Max Pacioretty scored for Montreal. Ben Scrivens made 36 saves.

"Probably credit to them and misreads by us," Pacioretty said. "We made a couple of mistakes, but it was a good bounce-back in the third."

Sheahan gave Detroit a 1-0 lead with 1:14 left in the first period. He backhanded in the rebound of Smith's shot.

It was the second time the Red Wings scored the first goal in their past 11 games.

"It definitely helps us. We went into the second with a little momentum," Sheahan said.

Mrazek stopped Pacioretty on a short-handed breakaway with 9:19 left in the first period.

Glendening and Sheahan scored 12 seconds apart early in the second period to make it 3-0.

Glendening beat Scrivens from the bottom of the right circle off a goal-mouth scramble 5:36 into the second for his seventh goal and third in four games. Sheahan's second goal of the game and 11th of the season came on a breakaway. He made a move on Scrivens and put a forehand shot under the crossbar.

"In the second period, they came at us with a lot of speed, and you can't forget ... on our back side (defensemen), we don't have a lot of experience," Canadiens coach Michel Therrien said.

Mantha scored a power-play goal with 2:33 left in the second period to make it 4-0. He put in a rebound for his first NHL goal. Mantha's parents were in attendance as well as his grandfather Andre Pronovost, who played for Montreal and Detroit during his NHL career.

Just 47 seconds into the third period, Plekanec made it 4-1 on a shot from the inside edge of the left circle that hit Mrazek and trickled into the net. It was Plakanec's 13th goal.

Byron made it 4-2 at 4:16 of the third when he poked in a rebound for his 10th goal.

Pacioretty's goal 7:50 into the third period pulled the Canadiens within 4-3. His shot from the right circle deflected in off the skate of Red Wings defenseman Niklas Kronwall. It was Pacioretty's 25th goal.

"We have to play 60 minutes. We knew it was going to be a battle in the third period," Mrazek said. "They scored two goals that were weird bounces that get them back into the game, but huge two points at the end."

NOTE: Montreal C David Desharnais returned after missing 17 games with a broken foot. ... Detroit came into the game tied for the final wild-card spot in the Eastern Conference playoff race with the Philadelphia Flyers, who had one game in hand. The Red Wings have made the playoffs the past 24 seasons. ... The Canadiens were also without D P.K. Subban (neck) and RW Sven Andrighetto (upper body). Subban is expected to return soon . ... Detroit's healthy scratches were RW Tomas Jurco, RW Teemu Pulkkinen and D Alexey Marchenko.