Stephen Curry scored 39 points for the Warriors after missing the previous five games with a left quadriceps contusion, but Minnesota held on even without injured star Anthony Edwards (right leg soreness).
DiVincenzo finished with 21 points, six rebounds and four assists in the first meeting between the teams since the Timberwolves eliminated the Warriors in the second round of last season's playoffs.
Julius Randle had 27 points, nine rebounds and six assists for Minnesota. Naz Reed added 18 points and seven assists off the bench.
Quinten Post scored 16 points for Golden State. Jimmy Butler had 15 points and eight rebounds.
There were 27 lead changes in the game, the second-most in the NBA this season, and both teams played shorthanded. The Timberwolves were without Edwards, and the Warriors were without the injured Draymond Green.
Minnesota gained momentum in the fourth quarter. The Timberwolves opened the final period on a 20-7 run and led by 10 with five minutes left before Curry and Moses Moody connected on back-to-back 3-pointers to push the Warriors to 108-104.
Golden State briefly led 118-117 on Curry's free throw with 1:37 remaining, but Gobert dunked and DiVincenzo made it 123-118 on his three with 28 seconds to play as the Wolves finished on a 10-2 run.
Curry quickly began his comeback. The two-time NBA scoring champion made his first three shots and scored eight of the Warriors' first 12 points.
Timberwolves: Host the Sacramento Kings on Sunday.
Warriors: Play the Trail Blazers in Portland on Sunday.
