Hundreds of loyal Timberwolves fans gathered at Target Center — and many more huddled around their television and smartphone screens elsewhere — shouted their hearts out Tuesday night when finally, thankfully, they no longer had a reason to be suspicious and fatalistic about the NBA’s covert draft lottery process.

But the two men deepest inside a whirlwind of emotion and celebration could barely speak when their team won the league’s No. 1 overall draft pick for the first time after 16 unsuccessful tries.

Timberwolves owner Glen Taylor choked up on a television stage in New York City when his franchise’s logo was the last one pulled out of envelopes and the league determined the Wolves, Los Angeles Lakers and Philadelphia will own the first three picks in a June 25 draft that features center Jahlil Okafor of Duke and Kentucky’s Karl-Anthony Towns.

A thousand miles away, Wolves coach and basketball boss Flip Saunders’ eyes welled with tears and his voice cracked when he talked about this past week. It started last Tuesday with the death of his father, Walter, back home in Cleveland and ended with Saunders and other grown men jumping for joy in the team’s arena players’ lounge after lottery results were revealed.

Until Tuesday, the Wolves never had done better in the league’s annual game of luck than they should have, and half the time they did worse. In 1992, for example, they could have turned the league’s worst record and most lottery chances into Shaquille O’Neal or Alonzo Mourning, but ended up with the third pick and Christian Laettner.

With Taylor representing the team at the lottery for the first time since he bought it in 1994, the Wolves now have their pick of the field to go along with 2013 first overall pick Anthony Bennett and 2014 overall No. 1 Andrew Wiggins, both acquired in trades.

“We waited 20 years to send Glen to the lottery, we should have sent him a lot sooner and as I said to our guys, my dad …,” Saunders said, choking on his words and pointing to the sky. “Sometimes you have to have luck.”

Saunders said with almost certainty that the team will not trade the No. 1 overall pick. He also said he doesn’t know who he will pick and said at this point it’s not merely a choice between Okafor and Towns, not with point guards D’Angelo Russell and Emmanuel Mudiay as well as European power forward prospect Kristaps Porzingis legitimate candidates as well.

“It’s not that simple,” Saunders said, referring to narrowing the field to the top two big men. “We have an idea but there are a lot of different directions we can go. … We have to rely on our ability to select the right players. This will give us great flexibility. Every spot you move up in the draft, you have more control over what’s going to happen and you have more people talking to you.”

Tuesday’s victory also gives Taylor, Saunders, their staff and their fans reason to believe the team is no longer cursed.

“I think it’s part of it,” Taylor said by phone about a celebration both at Target Center and New York City that seemed cathartic. “We’ve been cursed in the lottery and been cursed with injuries. Hopefully, we can get over both of those. We got over one of them. Now we need to get over the other.”

Taylor, who also owns the Star Tribune, said he attended the lottery for the first time because, as the league’s Board of Governors chairman, he wanted to see firsthand how the process worked. He sat on stage with representatives from 13 other teams as the draft order was revealed in order through 10 picks until the New York Knicks’ logo popped up out of place at pick No. 4.

Asked why it took him this long to represent his team and find some lottery luck, Taylor said, “Well, they never sent me out here before. You know, I shouldn’t have been asking for a free ticket. I should have paid for it myself, like I did today.”

The Wolves owned the best chance to win — 25 percent — among the 14 non-playoff teams participating, thanks to their league-worst 16-66 record that included a 12-game losing streak to end the season. Saunders suggested it was a hard sell convincing Taylor to build for the future when Ricky Rubio, Nikola Pekovic and Kevin Martin sustained serious injuries in November.

Now they can put their choice of prospects alongside a young group that already includes Rookie of the Year Wiggins, Zach LaVine, Shabazz Muhammad, Gorgui Dieng and Rubio.

“Well, it feels like it’s worth it right now,” Taylor said. “This will give us a spark and people will be excited. It’s a wonderful position to be in, that you can make the selection. But you have to do it right, now that we have this opportunity.”