Curry had 13 points in the fourth quarter as the Warriors came from nine points behind to win on back-to-back nights.
Andrew Bogut had 16 points, 17 rebounds and five assists to help overcome the loss of David Lee (shoulder, hip) and a horrendous shooting night from backcourt mate Klay Thompson, who was 3 of 20 for 11 points.
Reserve guard Alec Burks had with 26 points on a variety of jumpers and acrobatic drives but it wasn't enough for Utah, which dealt with injuries to three frontcourt players.
The Jazz played without starting forward Marvin Williams (heel), center Derrick Favors (hip) and starter Jeremy Evans left the game in the second quarter after a scary fall.
In a halftime ceremony, the Jazz honored Sloan, the Hall of Fame coach. They raised a banner at EnergySolutions Arena featuring the number '1223', which represents the combined number of Sloan's regular season (1,127) and playoff (96) victories in his 23 years as head coach of the Jazz from 1988-2011.
Karl Malone, John Stockton, long-time assistant Phil Johnson and Utah owner Gail Miller were among those who spoke during the festivities, which brought long periods of sustained ovations.
"I feel like I was the luckiest coach in basketball to have these players and the organization I had here," said Sloan, who won more games with one franchise (1,127) than any other coach. More than a dozen of his former players joined him on the court, including current head coach Ty Corbin.
The Jazz led 77-68 early in the fourth quarter, but the ragtag Jazz lineup collapsed against the onslaught of Curry's 3-pointers and Bogut's inside play during a 12-0 run that allowed the Warriors to reclaim the lead with 6:55 to play.
Jazz rookie Trey Burke was hampered with flu-like symptoms and foul trouble trying to stay with Curry and finished with four points. Reserve point Diante Garrett had a career-high 13 points.
Even when he was wide open, Thompson couldn't find his range but Curry was more than able to make the key plays.
Burks made a layup for Utah's final lead at 88-87 with 2:17 remaining.
Curry responded with a shot in the lane to spark a spurt of eight straight points to clinch the win for Golden State.
The Warriors have struggled since a 10-game winning streak in December and January, unable to string two wins together until the past two.
Evans was undercut on a rebound and landed on his back with 3:15 left in the first half. He laid still for a couple minutes and then gingerly walked to the locker room with assistance. Diagnosed with a bruised tailbone and right elbow, he missed the rest of the game.
The Jazz haven't played on the road since Jan. 18 at Minnesota, but they weren't able to extend their modest two-game win streak.
The Warriors missed David Lee. Lee, who averages 19.1 points and 9.