Curry made five 3-pointers and also added 10 assists for the Warriors, who had lost two straight and five of six.
Klay Thompson connected on a career-high eight 3-pointers and scored 28 points for Golden State. Harrison Barnes and David Lee had 11 points for the Warriors, who ended a four-game road trip with a 2-2 record.
In foul trouble throughout, DeMarcus Cousins had 24 points in just over 20 minutes. Marcus Thornton scored all of his 21 points in the second half for the Kings, who have dropped four straight and are now 3-7 at home.
Isaiah Thomas had 19 points and eight assists, but also committed seven of Sacramento's season-high 24 turnovers. Patrick Patterson scored 18 points and Jason Thompson added 10.
After Curry's free throws, Andrew Bogut blocked a driving layup by Thomas in the closing seconds and grabbed the rebound to secure the victory.
Trailing by two points twice with under a minute to play, Cousins responded with a pair of basket from close range, the second one tying the game at 113 with 12.6 seconds left.
A 3-pointer by Thomas put the Kings in front 104-102 with 3:51 left. But Thompson's corner 3 and a jumper by Curry put the Warriors on top, 107-106.
With the Kings down by 11 points, Thornton made a 3 to ignite a 12-2 run. Cousins ended the surge by converting a layup and making two free throws to cut Golden State's lead to 100-96.
After a strong first half, it was Thompson and Curry continuing their perimeter success in the third quarter, when they combined for five 3-pointers. Curry scored 11 points and Thompson had three 3-pointers and nine points, giving Golden State a 90-80 heading into the fourth.
Cousins was called for his fourth foul at the 7:45 mark of the third quarter. He argued the call and was quickly given his fifth technical of the season and went to the bench with the Kings trailing 66-59.
Warriors starting forward Andre Iguodala sat out his fifth straight game with a left hamstring strain.
Thompson benefited from many open looks in the first half when he made four 3-pointers and scored 16 points, helping the Warriors to a 56-53 lead. Curry was nearly as efficient, making three 3-pointers and scoring 13 points.
Despite limited playing time with three fouls, Cousins made all five shots and had 12 first-half points for Sacramento, which had 16 turnovers that led to 20 Golden State points.
The turnovers began early for the Kings, who had seven in the first quarter and committed another eight just past the midway point in the second quarter.
Notes: The arena power went out during pregame introductions and lasted for 12 minutes. When power was restored, the Kings' introduction was skipped and the game had no public address announcer until midway through the first quarter. . Historically, this has been a competitive matchup, with the Warriors holding a 187-185 edge. . Three Kings starters, including Cousins, had two fouls by the midway point in the opening quarter. . Warriors reserve guard Toney Douglas, who played with the Kings last year, has missed the last 11 games with a stress problem in his lower left leg.