They are closing in on an even more impressive mark.
Curry scored 31 points and the Warriors overcame a double-digit, second-half deficit for a 103-96 overtime victory over the Utah Jazz.
Golden State won its sixth consecutive game and second in as many nights. The Warriors (68-7) set a single-season franchise record for victories, topping the 67 they won last year en route to the NBA championship.
Klay Thompson forced overtime with a 3-pointer with 15 seconds left in regulation. He scored 18 points as the Warriors inched closer to the all-time-record win total of 72.
"They are amazing," Warriors coach Steve Kerr said of his players. "Nothing really went our way for most of the night, and they kept fighting, you know. We always compete. That's the great thing about this team. That's why we have this record. Our guys compete every night."
The Warriors need five wins in their final seven games to surpass the 1995-96 Chicago Bulls, who went 72-10, for the most victories in a single season.
Gordon Hayward scored 21 points and Rodney Hood added 20 points for the Jazz, who had won eight of 10 games.
"It was tough," Hayward said. "Felt like we played well enough to win tonight. Didn't get the plays we needed to down the stretch to secure the win, but they are a good team."
This was a disappointing result for the Jazz, especially considering they had a three-point lead with 24 seconds left.
Even more frustrating for Utah, though, was its performance from the free-throw line. The Jazz only made 13 of 29 free throws, a measly 44.8 percent, to blow a golden opportunity to put the Warriors away before crunch time.
Hayward shot 7-for-20 from the field and only made four of eight foul shots. Rudy Gobert, who had 11 points and 18 rebounds, and Derrick Favors, who finished with 15 points and seven rebounds, both went 1-for-4 from the line for Utah.
The Jazz were especially bad in the fourth quarter, when they missed 10 of 14 from the charity stripe.
"I know we were trying to make them. It wasn't effort," Jazz coach Quin Snyder said, trying to stay positive. "We didn't shoot well from the line. We can lament that fact or we can say we got beat by the world champs."
Hayward gave the Jazz an early lead in overtime, but Utah's offense wilted under the pressure after that.
Curry scored six straight points and Draymond Green (13 points) put the exclamation mark on the Warriors' win with a strong slam dunk for a 101-93 lead.
With 24.3 seconds remaining in regulation, Shelvin Mack gave the Jazz a three-point lead by splitting a pair of free throws.
After a timeout, Thompson missed an open 3-pointer, but Shaun Livingston snatched the offensive rebound and fed it back to Thompson. He didn't miss his second chance, tying the game with 15 seconds remaining.
The Jazz's final possession of regulation was awful, with Mack getting a hurried shot blocked by Green. Hayward caught the ball but badly missed a desperation heave at the buzzer.
"Our guys competed their (tails) off. We played so hard and played well," Snyder said. "I don't want the focus to be on execution on one specific play."
The Warriors knotted the score up at 85 after using the hack-a strategy to send Gobert to the free-throw line. The Jazz center missed both foul shots, and Green followed with an easy bucket.
Utah played most of the game without Favors. He sustained an ankle injury in the first half and then left for good with right knee soreness after being fouled hard by Andrew Bogut in the third quarter.
The Warriors took an early double-digit lead after a Leandro Barbosa bucket put them ahead 31-21 early in the second quarter.
Utah chipped away and momentarily overtook Golden State after a Hood 3-pointer. Harrison Barnes (15 points, 11 rebounds) responded with a 3-pointer, giving the Warriors a 42-40 halftime lead.
"It wasn't an easy game, obviously," Curry said. "We really had to battle all the way to the end. Klay hit a huge shot, and we got a big stop at the end of regulation. We used that momentum into overtime. The defense really carried us in overtime. It was a playoff kind of atmosphere. It was good."
NOTES: Four fans received minor injuries when a safety rail collapsed as spectators tried to get autographs from reigning MVP Stephen Curry after his pregame warmup session. Three of the fans were treated and released on the spot, while another visited an arena first-aid station but did not require medical assistance. Three of the fans received autographed items from Curry, including a shoe, a jersey and a basketball. ... Warriors coach Steve Kerr on his team's chances of breaking his 1995-96 Chicago Bulls' record of 72 wins in a season: "I've said many times over the years that I didn't think that record would be broken, and it still may not be. We have a tough finish still to go in the last games. To be part of both situations is unreal." ... The Warriors finish the season vs. Boston, vs. Portland, vs. Minnesota, vs. San Antonio, at Memphis, at San Antonio and vs. Memphis.