VANCOUVER, British Columbia -- The odds were stacked against the Detroit Red Wings at the start of Saturday’s game and got worse in the early going.

They were playing their second game in as many nights against the rested Vancouver Canucks. They dressed only 10 forwards because of injuries to

(head) and

(groin). And they fell behind by two goals less than 14 minutes into the game.

But the Red Wings persevered. They peppered goaltender Roberto Luongo with 54 shots and, amazingly, scored a buzzer-beating goal for the second consecutive night.

Henrik Zetterberg whipped in a backhand shot with 0.3 seconds remaining in overtime to give his team a 4-3 win at General Motors Place.

“No quit,’’ goaltender Jimmy Howard said. “We played until the final buzzer.’’

On Friday, Brian Rafalski scored with 0.2 seconds left in regulation against Edmonton, sending the game overtime. The Red Wings

, but this win eases the sting and sends them home from Western Canada with five of a possible six points and a two-point lead over the Calgary Flames for the final playoff spot in the Western Conference.

“We’re playing like this is the playoffs for us right now,’’ captain Nicklas Lidstrom said. “We’re really in need of points, so this is a huge one for us.’’

Todd Bertuzzi and Pavel Datsyuk scored 5 seconds apart in the second period, equaling the franchise record for the fastest two goals. Valtteri Filppula scored a shorthanded goal and added two assists.

Zetterberg had an assist to go along with his 20th goal of the season.

“Their (defenseman) broke his stick,’’ Zetterberg said. “Fil put it onto me, so I had a step on him and I didn’t know how much time was left, but it was enough.’’

Said Lidstrom: “At the end, we had almost all four guys in their zone pinching in, going towards the net, looking for chances, rebounds. You saw the desperation come out at the end in the last couple of games.’’

The Red Wings basically used three forward lines, occasionally playing defenseman Derek Meech up front. Defenseman Brett Lebda dressed but did not play.

“I thought we played real well,’’ Red Wings coach Mike Babcock said. “Even when we were down 2-0, I thought we were the better team in the first period. Our guys just kept playing. Anytime you’re on the road and you generate the amount of opportunities we did, we must have done a lot of good things.

“I thought Z and Pav were absolutely fantastic; Rafi (Brian Rafalski), Nick (too), and Fil had a real good night for us. We know we got to get points and I thought our guys played hard. I told our coaching staff I really thought we’d dig in here tonight.

“We outplayed them from the start to the end.’’

Despite outplaying the Canucks by a wide margin early, the Red Wings trailed 2-0 until they finally got a break on Bertuzzi’s goal at 12:34 of the second period.

Filppula threw the puck in front of the net from the side. It hit Kevin Bieksa’s leg and sat in the crease. While the defenseman was searching for the puck, Bertuzzi whacked it into the net to end his 19-game goal-scoring drought, which dated back to Jan. 23.

“It was more fun scoring in this building (against his former team) than the relief of actually getting one,’’ Bertuzzi said. “I just tried to get to the net for Z and Fil, and we had a handful of chances tonight.’’

Then, off the ensuing faceoff, Datsyuk took the puck into the Vancouver zone and whipped a wrist shot from the slot past Luongo at 12:39 to tie the game and tie the club record for the quickest two goals (set by Tomas Holmstrom and Datsyuk on Nov. 24, 2007). It also is the fastest two goals allowed in Canucks history.

Filppula snapped the tie by scoring on a breakaway while shorthanded at 17:39. Defenseman Alex Edler stumbled at the Detroit blue line, enabling Filppula to break in alone and deposit a backhand shot past Luongo.

The Canucks applied heavy pressure at the start of the third period and tied it on Daniel Sedin’s goal at 4:40. Sedin gloved a deflected pass from Bieksa, knocked the puck down and swatted it into the net.

The Red Wings outshot the Canucks 17-8 in the first period, controlling the play for a good portion of time in the offensive zone and getting some quality scoring chances.

But they trailed 2-0 after Vancouver scored twice on shots from the point through traffic.

After the Canucks killed an early penalty, Kyle Wellwood opened the scoring with a blast from the right point that found its way past a few bodies and through Howard’s five-hole.

Shane O’Brien scored on a wrist shot from the left point at 13:38.

But there was plenty of time left for the Red Wings.

“It’s a never-die attitude,’’ Bertuzzi said. “Guys are playing well right now. We responded with a big two points.’’