NEW YORK — The Minnesota Timberwolves too often came to the NBA draft lottery and left in worse shape than they arrived.

And when they finally ended years of lottery futility, it came from the spot where nobody had been winning.

The Timberwolves won the lottery Tuesday night, the first time since 2004 the team with the worst record earned the No. 1 pick.

After years of bad luck, things finally worked out for the Wolves, who can perhaps choose between big men Karl-Anthony Towns of Kentucky and Jahlil Okafor of national champion Duke to put next to Rookie of the Year Andrew Wiggins.

“We’re in this for big stakes,” said Flip Saunders, the Wolves’ president and coach. “The big thing about this is getting good talent that can blend together. This is another big step.”

The Los Angeles Lakers moved from the fourth spot to second, keeping a pick they would have sent to Philadelphia if it fell outside the top five. The 76ers are third followed by the New York Knicks, who had the second-best odds of winning but instead fell to fourth 30 years after winning the first lottery and drafting Hall of Famer Patrick Ewing.

Not since Orlando won the right to pick Dwight Howard in 2004 had the NBA’s ultimate game of chance came out in favor of the team with the best odds. The Timberwolves had a 25 percent chance of landing the top pick after finishing 16-66.

But their fans knew not to get their hopes up after the Wolves had fallen backward eight times previously, including both times they were in the pole position. A chance at Shaquille O’Neal turned into Christian Laettner in 1992, and they fell one spot in 2011 to miss out on Kyrie Irving.

“Today was very nerve wracking. I really didn’t anticipate that it would go this way,” owner Glen Taylor said. “People say you have a 25 percent to win but I always look at it that there’s a 75 percent chance that someone else is going to win. I just feel very honored that we have the chance to be in this position.”

Several hundred fans gathered to watch on the big screen at Target Center in Minneapolis and erupted when the Lakers card came out of the envelope for No. 2, meaning Minnesota had finally earned the top pick for the first time.

The Lakers were the other big winners even without moving all the way to the top. Their pick was only protected in the top five as a condition of their trade with Phoenix for Steve Nash in 2012. That was dealt this season to the 76ers, who could have ended up with two top-six picks if the Lakers had fallen backward two spots.

“I told our guys earlier today that I had a real good feeling about tonight,” Lakers coach Byron Scott said. “I hope not to be back here anytime soon, but I’m happy the way things turned out tonight.”

So was superstar Kobe Bryant, who ended his tweet after seeing the results with (hash) lakerluck and (hash) goodday.

The lottery sets the top three picks. The remainder of the 14 non-playoff teams follow in inverse order of their won-loss record.

Things went according to form until the Knicks slid. General manager Steve Mills hoped history could repeat by wearing Dave DeBusschere’s Naismith Memorial Basketball Hall of Fame ring, which DeBusschere was wearing as the Knicks’ GM when they won the 1985 lottery.

“Obviously, we would have liked to receive a higher pick but we went into this knowing that anywhere between one and five we were going to get a good pick,” Mills said.

The lottery began 30 years ago as a way to discourage teams from losing on purpose as a way to secure the top pick. Tanking may still exist — the 76ers have appeared to be angling for the draft with no regard for their record the last couple of seasons — but the Wolves appeared to lose honestly while battling numerous injuries with a young roster.

Their victory, with Taylor on stage, was only the fifth time the team that finished with the worst, or tied for the worst record, won the lottery.

Saunders, who got emotional talking about the recent death of his father, joked that the Wolves shouldn’t have waited so long to have Taylor represent them. He almost didn’t, as he sought to have his wife, Becky, do it but the league sent a memo saying it didn’t want family on stage.

“Glen, reluctantly I think, went up there,” Saunders said. “He’s good luck. Glen always has a tendency to be pretty lucky. He did what he had to do.”

The Cleveland Cavaliers had won the last two and three of the previous four lotteries since LeBron James left them for Miami in 2010. They drafted Wiggins last year but dealt him, along with 2013 No. 1 Anthony Bennett, to the Wolves in the deal for Kevin Love.

With James back home, the Cavaliers are in the Eastern Conference finals and Miami was in the lottery, and the Heat held in the No. 10 spot where they entered.

The Heat’s pick would have gone to Philadelphia if they fell out of the top 10.