VANCOUVER, British Columbia — Daniel and Henrik Sedin created a note-perfect home finale to their extraordinary 17-year N.H.L. careers with the Vancouver Canucks.

On Thursday, Daniel scored twice, including the overtime winner, and Henrik assisted on both goals as the Canucks beat the Arizona Coyotes, 4-3. The sellout crowd at Rogers Arena chanted “Go Sedins Go!” and “Hall of Fame!”

Even though the Canucks will miss the playoffs for the fourth time in five years, Vancouver fans showed their appreciation for the 37-year-old identical twins from Sweden.

“It was really nice the way things ended and how the game went,” said Henrik, the Vancouver captain. “When you get a chance to go through this, it’s just once in a lifetime. You can’t describe the feeling.”

The Sedins, two former N.H.L. scoring champions who announced their retirements on Monday, had said they wanted to treat their last home game like any other game. Yet it was hard to keep things low-key amid standing ovations, thunderous Viking claps, and blue and yellow lights across Vancouver paying tribute to their Swedish heritage.

The timing of their retirement announcement was intended to give the Canucks a chance to celebrate the Sedins’ legacy without setting the stage for a lengthy farewell tour. The twins, who will play their final N.H.L. game on Saturday in Edmonton, are in the final year of their contracts.

“Over the years, it’s always been the two of us,” Daniel said. “We came in as teammates, and we should leave as teammates too. I think that’s never been a question.”

The brothers, born in Ornskoldsvik, Sweden, have reaped accolades for their unusual, creative style and their staggering statistics. Henrik is the Canucks’ career scoring leader with 1,071 points, and Daniel is second with 1,038 points. Their consistency has been their hallmark; this season, Daniel has 55 points to Henrik’s 50.

“If they can say that we always came into practice or games the same way, win or lose, whether we had two goals or were minus-4, that’s something we really take a lot of pride in,” Daniel said.

Since their rookie season of 2000-1, at least one Sedin has appeared in every Canucks game, including 1,359 regular-season contests and 105 in the playoffs.

Drafted second and third over all by Vancouver in 1999, the Sedins were not defined by big hits, last-minute goals or shootout success. Instead, they specialized in magical games of keep-away, whether cycling the puck down low or making no-look passes on the rush. When they got into “Sedinery” mode, finding each other intuitively, highlights happened.

The approach helped the Sedins become the only brothers in the 1,000-point club. On Nov. 30 against the Nashville Predators, Daniel surpassed 1,000 career points. Henrik, who has had fewer injuries, hit that milestone in January 2017. Only 87 N.H.L. players have scored 1,000 points.

The spotlight was unavoidable during Vancouver’s glory years. The club won the Presidents’ Trophy as the N.H.L.’s top regular-season team in 2011 and 2012. In 2010, Henrik, a puck-moving center, won the Hart Trophy as the league’s most valuable player and the Art Ross Trophy as the top scorer with 112 points. In 2011, Daniel, a slick left winger, led the league with 104 points, and won the Ted Lindsay Award, the Most Valuable Player Award voted by the N.H.L. Players’ Association.

But the Canucks got close to winning the Stanley Cup only once in the Sedin era, in 2011, when they lost to the Boston Bruins in seven games.

“We wanted to be the go-to guys who took a lot of criticism when things didn’t work out, but also the guys who made plays that won us games,” Henrik said. “It’s something we never shied away from.”

The Sedins were criticized for being too honorable for their own good. Notably, Daniel let the Bruins’ Brad Marchand punch him repeatedly in the 2011 Cup finals. Daniel, who said that he obeyed instructions from Alain Vigneault, then the Vancouver coach, to stay disciplined, described that final as “probably the highlight of our careers and also the lowest part of our careers too.”

The twins struggled with the pace of the playoffs at times. In other series, lesser agitators than Marchand, like Dave Bolland of the Chicago Blackhawks and Micheal Ferland of the Calgary Flames, were able to limit the Sedins’ effectiveness.

Trevor Linden, the Canucks’ team president, who played six seasons with the Sedins late in his career, was impressed by how the Sedins persisted against physical, stick-wielding defensemen.

“I remember thinking that they never changed the way they played,” Linden said. “They were never intimidated by the other team with how they were played or treated by defensemen. They were just steady as the day is long.”

After the 2004-5 N.H.L. lockout, the twins’ skating improved drastically, and they were always the fittest players at Vancouver’s training camps — “by a mile,” Linden said. The Sedins’ increased offensive production erased thoughts of returning to Sweden, which had lingered after their lackluster third N.H.L. season.

They also decided to stay in Vancouver instead of chasing bigger dollars or a chance to win the Stanley Cup in another market.

“We both felt that if we didn’t make the playoffs here, it doesn’t feel like winning the Stanley Cup with a different team, going there for a couple of months,” Henrik said. “We said it wouldn’t be the right way for us, and we’ve stuck with it. We believe we made the right choice.”

Embedded in Vancouver, they endeared themselves both to the news media with their amiable, reliable availability and to the fans with generous acts like donating $1.5 million in 2010 to build a new children’s hospital.

The Sedins are likely bound for the Hockey Hall of Fame, especially after winning gold medals at the 2006 Olympics and 2013 world hockey championship, but their overall legacy will be debated. They were trailblazers in a league where puck possession is increasingly important, but their telepathic style is as inimitable as Dominik Hasek’s acrobatic style was for goalies.

“From Day 1, it’s been so impressive watching them on a daily basis, just what they do, not just on the ice but off the ice, how professional they are, how hard they work in the community,” said Alexander Edler, a fellow Swede and teammate since 2006. “I think just being around those two every day really helps the other guys, and it helped me a lot.”