Roberto Luongo puts Canucks one win from their first Stanley Cup

Canucks goaltender Roberto Luongo put on a hoodie and headphones and went for a walk along Vancouver’s scenic seawall Friday afternoon. He had gone down that path before he faced the Chicago Blackhawks in the seventh game of the first round of the playoffs, but this trip was different.

He had yielded 12 goals in Boston while the Bruins tied the Stanley Cup finals at two games each, rekindling questions about his big-game credentials. Burrowed into that hoodie, oblivious to everything around him, he took a stroll after the team’s pregame meal. He went to look inside himself, not at the picturesque waterfront and majestic mountains.

“Sometimes I need to clear my head and put things in perspective,” he said. “I just focus on the journey and everything I need to do to be ready for the game.”

He was ready from start to finish, stopping 31 shots by the Bruins in a 1-0 victory at Rogers Arena that moved the Canucks within one triumph of winning the Stanley Cup.

The Canucks can bring the Cup back to Canada for the first time since 1993 if they win Game 6 on Monday at Boston’s TD Garden. A seventh game, if necessary, would be played Wednesday in Vancouver, a city that has waited four decades to claim hockey’s most cherished prize.

In the 21 previous finals that were tied at 2-2, the winner of

Game 5 won the Cup 15 times (71%). But the Canucks have made this difficult on themselves. They have been outscored, 14-6, in the first five games — the record for fewest goals in six games of the Cup finals is nine, done twice — yet have made their goals count.

Maxim Lapierre, dealt by the Ducks to Vancouver at the trade deadline, provided the only goal of a fast and physical game at 4:35 of the third period. Defenseman Kevin Bieksa shot the puck wide of the net in hopes of a fortunate carom and got it, as Lapierre snared the puck deep on the left side and flipped it past Boston goalie Tim Thomas.

That ended Thomas’ shutout streak at 110 minutes 42 seconds over three games, energized the crowd and triggered celebrations among thousands of fans gathered to watch the game on huge video screens in downtown Vancouver.

“He played an unbelievable game for us, but we expected it out of him,” Bieksa said. “It’s no surprise. He’s a big-time goalie. He’s been on the big stage before.”

This was Luongo’s second 1-0 shutout in the finals, following a 36-save performance in Game 1. Luongo and Toronto’s Frank McCool, in 1945, are the only goalies to record two 1-0 shutouts in the finals.

Every game of this series has been won by the home team. If the Canucks can’t break that pattern Monday they’ll get another chance Wednesday in front of fans whose long-held cynicism just about vanished in the face of Luongo’s resilience.

“You can’t really blame him for what happened in Boston. It was the whole team that let down,” Bieksa said. “You saw the whole team regroup and come back and play strong.”

The Canucks had to kill three straight penalties in the first period and killed four Boston disadvantages overall. “I thought we all played well and stepped it up to a new level,” Luongo said.

The Bruins took comfort in going home, where they’ve thrived. “We have to look at that as a positive,” winger Milan Lucic said. “We’ve worked hard all year to get to this point. We’ve got to find a way to do it and dig deep to do it.”

Luongo already has his Game 6 strategy planned out.

“I don’t know if they have any seawalls in Boston” he said, “but I’m going to look for that.”

helene.elliott@latimes.com