Rush's 23-footer with 1:09 remaining in the fourth quarter put Golden State ahead 90-88 and the Warriors hung on to snap an eight-game losing streak.
Rush finished with 19 points and nine rebounds while Klay Thompson added 17 points for the Warriors, who recovered from a 21-point second-quarter deficit.
Nikola Pekovic supplied 19 points and 16 rebounds for the Timberwolves, who lost for the 12th time in 13 games.
Martell Webster scored 18 points in Minnesota's setback.
Swim Week Miami Beach 2014 [PHOTOS]