Karl-Anthony Towns scored 36 points and added 14 rebounds on the night for Minnesota, including a 23-foot jumper with 1:06 left which forced overtime.
In the extra period, Irving had four points but missed a 15-foot shot with 14.5 seconds left as the Nets went down in their season opener.
The Philadelphia 76ers starters played strongly, with Ben Simmons scoring 24 points and Joel Embiid adding 15 as they beat the Boston Celtics 107-93.
Elsewhere, the Charlotte Hornets pipped the Chicago Bulls 126-125, Andre Drummond got 32 as the Detroit Pistons saw off the Indiana Pacers 119-110, while Nicola Vucevic led Orlando Magic to a 94-85 win over the Cleveland Cavaliers.
The Miami Heat beat the Memphis Grizzlies 120-101, Luka Doncic had 34 points for the Dallas Mavericks who beat the Washington Wizards 108-100 and the San Antonio Spurs defeated the New York Knicks 120-111, on a night when Gregg Popovich became the first man to coach one side for 24 seasons.
There were also wins for the Utah Jazz, 100-95 over the Oklahoma City Thunder, Nikola Jokic had 20 points and 13 rebounds in a 108-100 win for the Denver Nuggets over the Portland Trail Blazers and the Phoenix Suns cruised past the Sacramento Kings 124-95.