The Warriors, just one season removed from a run of five straight finals appearances that yielded three titles, garnered the second overall selection.
As the teams with the worst three records in the season, Minnesota, Golden State and the Cleveland Cavaliers each had a 14 percent chance of winning the first overall pick.
Cleveland, however, fell to fifth as the Charlotte Hornets, owned by NBA icon Michael Jordan, rose from eighth in the pre-lottery odds to earn the third overall pick.
The Chicago Bulls will pick fourth followed by the Cavs, Atlanta Hawks, Detroit Pistons, New York Knicks, Washington Wizards, Phoenix Suns, San Antonio Spurs, Sacramento Kings, New Orleans Pelicans and Boston Celtics.
Unlike last year, when Zion Williamson was the clear favorite to be selected first overall, this season's potential top picks include guard LaMelo Ball, who most recently played in Australia and whose brother Lonzo plays for the Pelicans, University of Georgia star Anthony Edwards and University of Memphis standout James Wiseman.
"We couldn't be more pleased to land the first overall pick in this year’s draft, marking only the second time in franchise history," Timberwolves President of Basketball Operations Gersson Rosas of Colombia said.
"We are excited for the possibilities ahead of us to bring in a high caliber player now that we secured the first overall selection. We know with the number one pick we have the opportunity to draft an impact player who could immediately complement our young, strong core in All-Star center Karl-Anthony Towns and All-Star guard D’Angelo Russell."
NBA Commissioner Adam Silver took the opportunity of the televised lottery, which came as the NBA played first-round playoff games in a quarantine bubble in Orlando, Florida, to address potential changes to plans for the 2020-21 season, which had been projected to start on December 1.
Silver said the league is not focused on playing in a fan-free campus next season, but hopes to have fans in their home stands.
"I'd say December 1, now that we're working through this season, is feeling a little bit early to me," Silver told broadcaster ESPN.
"I think our number one goal is to get fans back in our arenas... So my sense is, in working with the Players Association, if we could push back even a little longer and increase the likelihood of having fans in arenas, that's what we would be targeting."
Silver's comments followed an ESPN report that the NBA players' union had been advising players that the start of free agency could be delayed from its scheduled launch on October 18, although the draft remains scheduled for October 16.
The NBA Finals are slated to end in Orlando no later than October 13.