Curry put Golden State in front to stay with 2:02 remaining and wound up making 8-of-13 from long range.
Utah jumped in front by nine points early in the fourth quarter before Golden State went on a 12-0 run to make up the deficit.
The Jazz regained the lead for the final time at 88-87 on a layup by Alex Burks with 2:18 to go, but the Warriors then ran off eight straight points to seal the victory.
Utah's last chance came as the game entered its final 30 seconds. The Jazz had the ball trailing by three, but Gordon Hayward suffered a turnover and Curry hit two foul shots with 22.7 seconds left to give the Warriors a five-point cushion. The Jazz lost for the 30th time this season.
Curry's previous season high had been 43 points, scored in a loss to Charlotte on Dec. 9.
Andrew Bogut added 16 points and 17 rebounds for the Warriors. Utah was led by Burks with 26.