– Minutes after his team ambushed him with birthday cake, Rocco Baldelli wore what looked like a gooey crown slathered on his forehead. He did not hurry to remove it.

On Wednesday, the Twins’ manager turned 38, his team won its 98th game, and his birthday celebration became the opening act for a championship party. Cake was washed away by champagne.

All season, Baldelli has watched diverse ingredients gel into something sweet and surprising. The Twins entered Wednesday’s play needing a victory and a Cleveland loss to clinch their first division title since 2010. They beat Detroit 5-1, then watched from a room adjacent to the visitors clubhouse at Comerica Park as Cleveland lost 8-3 to the White Sox.

Twins players screamed in multiple languages and doused each other with beer and champagne, stars hugging reserves who were hugging newcomers who began the year in the low minors.

“It’s not one guy,” Nelson Cruz said. “It takes the whole organization. The guys across the minors, the trades, everything, for you to get here.”

On a night when “launch angle” measured flying corks, the Twins honored unusual career trajectories.

On May 16, Miguel Sano returned to the big leagues after recovering from a cut on his heel, and Luis Arraez had yet to make his big league debut.

On July 21, Trevor May had an ERA of 4.10.

On July 23, Tyler Duffey’s ERA rose to 3.82 in a 14-12 loss to the Yankees.

On Aug. 8, Randy Dobnak was a former independent league pitcher who had yet to make his big-league debut.

On Sept. 25, those formerly under-or-off-the-radar players produced, again, proving that the most mathematic of sports is often the least predictable. A player can change a grip or a thought and alter a season or a career.

In the seventh inning, with the Twins trailing 1-0, Sano drew a walk, Arraez lofted a home run into the right-field seats, and Duffey relieved Dobnak, striking out two in a shutout inning. Duffey has not allowed a run since that game against the Yankees.

May pitched a perfect eighth inning, giving him a 1.38 ERA over his past 26 innings.

In mid-May, Sano was a franchise problem, Arraez a relative unknown and Dobnak a certified unknown. May and Duffey were symbols of bullpen failure.

“It’s extremely rewarding,” Baldelli said. “Rewarding is a nice word, but it means something to you. It means something to the organization.

“When you look up and see guys that we have that are stars, guys that are not on the field right now, guys that have done great things for us this year, it would be easy to make an excuse or say, ‘Well, we’re not going to get the same type of production from whoever fills in.’

“That’s completely contrary to the way we’ve gone about everything this year. It’s not even a thought in the mind of any person in the clubhouse, player or staff member. We expect every person that we send out there to go out and compete and produce and win games.”

During the celebration, Baldelli wore a championship hat as he made his way to the corner where the Twins’ big bosses — Jim and Joe Pohlad and Dave St. Peter — stood. Baldelli expressed thanks as foam flew around him.

Later, the team took to the still-lit field to pose for photos, and reliever Sergio Romo ran shirtless across the outfield.

“We knew in spring training we had a talented group,” Baldelli said. “We didn’t know how it was going to play out. But we did look up and say, ‘Wow, we’re going to have some guys that are going to help us this year. They might not be there at the very beginning, but they’re going to help us.’ And they’re helping us right now.”

Dobnak pitched in the clincher and will get married this weekend. When he returns, the former Utica Unicorn might start in a playoff game.

Sure, it takes a village, but a village this big?