If the Winnipeg Jets want to believe there is hope of a longshot, late-season playoff push, beating the Canucks in Vancouver Wednesday night was an absolute must.

Mission accomplished, albeit barely, as Cole Perfetti’s first career overtime goal was the difference in a 3-2 win coming out of the Olympic break.

With Josh Morrissey, Neal Pionk, Nino Niederreiter and Connor Hellebuyck out of the lineup, the game got off to a shaky start for the Jets as they fell behind just 1:58 into the contest.

Logan Stanley tried to clear the puck out of his end but his weak chip up the ice was grabbed out of the air by Brock Boeser. He sent it to a wide-open Drew O’Connor in the slot, whose shot squeezed through the five-hole of Eric Comrie and into the net.

Winnipeg nearly equalized the contest on the power play roughly eight minutes into the period but Cole Perfetti’s chance from the slot hit the crossbar.

A few minutes later, the Jets did respond thanks to one of their Olympians.

The play began when an Evander Kane pass out of the Vancouver end went awry, allowing Mark Scheifele to collect the puck and skate into the Canucks’ zone. He passed it off to Dylan DeMelo in transition, whose shot was blocked into the corner, but Kyle Connor won the battle for the puck and gave it to Scheifele.

As Scheifele carried it behind the net, he dropped a behind-the-back pass to Connor, who quickly got in front and snapped it into the goal for his 26th of the season, adding validation to his decision to return to Winnipeg team immediately after arriving in North America from Italy.

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The game went to the first intermission tied 1-1, with Winnipeg outshooting the Canucks 8-7 in the opening period.

But just 38 seconds into the middle frame, the Canucks reclaimed the lead. Elias Pettersson won a faceoff in the Winnipeg end back to Kane, who quickly fired a shot that beat Comrie high to make it 2-1.

The rest of the period was all Winnipeg, though for the most part, they had nothing to show for it. They failed to convert on two more power plays against the league’s worst penalty kill, but had the puck in Vancouver’s end for most of the period until finally breaking through with 1:15 to go.

The puck found its way to Luke Schenn at the point in the Canucks’ end before the veteran blueliner sent it to a wide-open Scheifele at the faceoff dot. He held the puck for a few seconds as traffic converged around Vancouver goalie Nikita Tolopilo before sending a pass to the goalmouth that ricocheted off Gabriel Vilardi and into the net.

Winnipeg wound up outshooting the Canucks 13-4 in the second but the game remained tied heading to a third period that was dominated by the home team.

It was Vancouver’s turn to strike iron just over four minutes into the third when Filip Hronek beat Comrie from the point but the shot rang off the post and careened away from danger.

Another great chance for the Canucks came just past the midway point of the third when they broke free on a 2-on-1. Comrie stopped the initial shot from Marco Rossi and the rebound appeared to be available for Conor Garland but right before he could shoot it, a backchecking Vladislav Namestnikov dove to knock it away.

Just over a minute later, the Jets were called for their first penalty of the night as Connor picked up a minor penalty for high-sticking but Winnipeg killed it off.

The Canucks wound up outshooting the Jets 11-3 in the third but the two sides needed overtime to decide a winner.

Each team had decent looks to score before Perfetti played the role of hero. Adam Lowry drove the puck deep into the Canucks zone before trying to centre the puck. It took a touch off the stick of Tolopilo and right to the stick of Perfetti, who wired it home from the slot for his third goal in his last four games.

Comrie turned aside 21 shots in the win, including one just moments before Perfetti scored the winner.

The Jets will get Hellebuyck back for their next game in Anaheim on Friday night. The puck will drop just after 9 p.m. with pregame coverage on 680 CJOB beginning at 7 p.m.