– The Timberwolves made Kentucky’s Karl-Anthony Towns the NBA draft’s first overall pick for the first time in franchise history Thursday because they deem him a uniquely skilled big man who handles and shoots the ball like a guard, unquestionably the most talented player available.

But it’s a good thing they didn’t ask him to hoist a shot just before he walked onto a stage at Brooklyn’s Barclays Center and hug NBA Commissioner Adam Silver while his mother and sister cried at a nearby table.

College coach John Calipari sat at the Towns family’s table on a night he helped soothe and send six of seven eligible Kentucky players — including four in the first 13 picks — to the next stage of their careers.

“I was trying to drink the water and I was shaking uncontrollably,” Towns said, “and I told him, ‘Coach, don’t give me the ball right now for the last-second shot. I wouldn’t make it.’ ”

The Wolves chose Towns over Ohio State guard D’Angelo Russell (second to the L.A. Lakers) and Duke center Jahlil Okafor (third to Philadelphia) after basketball boss Flip Saunders watched him work out in Los Angeles and then brought him to the Wolves’ new training facility for a visit that won over owner Glen Taylor and left no doubt in Saunders’ mind that they were taking the draft’s best player.

– and will pair him at point guard with starter Ricky Rubio. The Wolves traded three second-round picks — their 31st and 36th overall Thursday, plus one in 2019 — to the Cavaliers in a deal that created bedlam at Jones’ celebration party in a downtown Minneapolis restaurant.

Saunders called the selection of Towns “a home run.”

Towns used the word “awesome” when he discussed the prospect of playing professionally with Jones and “amazing” when asked about the prospect of playing with Rubio, whom he called “one of the best pass-first point guards in the league.”

Rubio welcomed the new guy to the Wolves with a tweet that asked if he was ready to pick up Rubio’s dry cleaning in the morning.

“I heard,” Towns said. “I’m just ready to be a rookie and help contribute to my team.”

Towns compared his new team to his old one, a talent-rich Kentucky team that went 38-0 before losing a Final Four semifinal game to Wisconsin.

“It reminds me a lot of Kentucky,” Towns said. “As soon as we come together, I think we could be a force to be reckoned with.”

Saunders in turn called Towns’ improvement the last year “astronomical,” praised his presence around other players, called Towns’ L.A. workout probably the second-best he’s ever seen after one in 1995 by another 19-year-old, Kevin Garnett.

“It’s everything,” Saunders said. “He plays with a great passion. He plays hard. He’s multiskilled. When you see him warming up, you’re going to think we drafted a point guard.”

The whole world knew the center was Minnesota bound but Towns himself vowed Thursday, as he had the day before, that he didn’t know he’d be the draft’s top pick until he saw “a man” walk to the lectern and call his name before all others.

A crowd estimated at 8,000 fans gathered to share the excitement at Target Center for a draft viewing party. They buzzed 30 minutes before Silver stepped on stage, booing when long-gone Kevin Love’s image was shown on the scoreboard screen and cheering for Rookie of the Year Andrew Wiggins.

Born and raised in nearby New Jersey, Towns celebrated Thursday in Brooklyn with nearly 50 family members and friends in attendance, only two years after his parents sat in bleachers and watched him play high school games. Now he is the third Kentucky player — following John Wall and Anthony Davis — drafted first overall in the past five years.

He wore a gray and white herringbone jacket with leather accents, black shirt, black pants and no tie, an outfit chosen specially for his big night by Towns’ “stylist.”

“There’s eight meters of this fabric in the world and this suit is 2½ of it,” Towns said. “He really blessed me with a one-of-a-kind suit for this special day in my life.”

Before Towns reached the stage, his American father and Dominican mother already wore Timberwolves hats along with their son, who quickly promised Timberwolves fans he’s ready to start a “personal quest” to reach the playoffs for a franchise that hasn’t done so since Garnett took them to the Western Conference finals in 2004.

He joins a list of former No. 1 overall picks that includes Magic Johnson, Shaquille O’Neal and LeBron James and joins an organization for which Dominican Republic-raised Felipe Lopez once played.

“It just means the world to me,” he said about both distinctions. “I’m just blessed to be in this opportunity to show a boy from Piscataway, New Jersey, and Dominican Republic can make it,” he said. “I’m blessed to be in this seat talking to you. It just means the world that I’m going to be able to show kids around the world that with a little hard work, determination, a little bit of luck and some determination, you can really make it far in this world.”