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.
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