The Timberwolves and Denver Nuggets played 82 games to settle a playoff score. And when 48 minutes wasn’t enough Wednesday night, they played five minutes more.

At the end of overtime, the Wolves prevailed 112-106 at Target Center, earning their first appearance in the NBA playoffs since 2004.

Their leader Jimmy Butler implored Wolves teammates all season to play a complete game, and on its final day, they delivered a defining victory that ended the Nuggets’ six-game winning streak and sent Denver home for the summer.

Playing only the third such winner-take-all game in the NBA regular-season finale since 1984, the Wolves played before the 16th sellout crowd of the season, the franchise’s most since its infancy in 1992.

“No boos, thank goodness,” Butler said, referring to Monday’s victory over Memphis, before praising his team. “Our guys, their hearts are pure. They want to win. They want to do what’s best for this organization, this city. They did that tonight.”

The Wolves finished with 47 victories, 16 more than last season’s 31. That was only enough to earn the eighth seed in the Western Conference by one game over Denver, earning them a playoff matchup with the top-seeded Houston Rockets.

Still, it will be the franchise’s first playoff game since Kevin Garnett, Sam Cassell and Latrell Sprewell reached the Western Conference finals so long ago.

This current group is going where Wolves such as Randy Foye, Corey Brewer, Kevin Love, Ricky Rubio, Derrick Williams and Zach LaVine never went before.

“We played whatever 48 plus five is,” Butler said after scoring 31 points in 42 minutes in only his third game back from right knee surgery. “We played that many minutes of basketball. I’m glad to see that, finally. Let’s keep it going. It’s no different now.”

The Wolves stopped unstoppable Denver center Nikola Jokic — who finished with 35 points, including 17 in the third quarter — just long enough to force overtime. Once they got there, the Wolves outscored the Nuggets 11-5, holding them without a point for the final 2 minutes, 28 seconds, outscoring them 7-0 in that time.

They did so with Karl-Anthony Towns’ play, as he approached Jokic’s numbers with 26 points and 14 rebounds, his league-best 68th double-double this season.

“I’ll probably fall asleep tonight and wake up in middle of the night and start crying,” Towns said. “It’ll hit me what happened.”

Video (05:16): The Timberwolves' 112-106 victory over Denver on the season's final night send them to a playoff series against top-seeded Houston while the Nuggets go home for the summer Video (05:16): The Timberwolves' 112-106 victory over Denver on the season's final night send them to a playoff series against top-seeded Houston while the Nuggets go home for the summer

They did so with Taj Gibson’s valiant defensive performance against Jokic and others, two nights after the veteran forward left early against the Grizzlies because his neck was too sore to turn his head.

They did so with Jeff Teague’s 17 points, including a short floater to put the Wolves ahead to stay at 107-106 with 1:18 with OT, after Denver had taken the second of its two one-point leads in the extra period. Teague also hit a three-pointer to put the Wolves up 99-91 with 4:26 left in regulation, but Denver went on a 10-2 run to close the fourth quarter.

And they also did so with Andrew Wiggins redeeming himself at the free-throw line — a nemesis on occasion — by making two crucial ones with 14.6 seconds left in OT.

“Everyone played a part in this win, everybody,” Towns said. “For everything that has been said about Wigs, he came out and gave us the win. He hit those free throws. Those were the biggest shots not only of the night but possibly of his career. He did his job. Everybody did their job.”

Funny, but “Do Your Job” is one of coach Tom Thibodeau’s favorite catchphrases, of which there are too many to count.

Butler did his, providing the kind of two-way play — those 31 points along with five rebounds, five assists and a steal — for which he has become acclaimed.

Tuesday, Wiggins had said the team’s entire season would have been a failure if the Wolves didn’t win Wednesday and reach the playoffs, in which the franchise last played when he was a fourth-grader in Toronto.

He has reached his first postseason in his fourth NBA season.

“It means a lot,” Wiggins said. “We’ve been at it for a long time. This is the first one. When I came here, finally there now, everyone in Minnesota is happy.”