Draymond Green knocked down his first four 3-point tries in the opening 3 1/2 minutes on the way to 29 points, 17 rebounds and 14 assists for his NBA-leading sixth triple-double.
"That’s the MVP of the league, and we need him," Green said of Curry. "That’s no secret, but guys stepped up and made plays."
About 10 minutes after the game ended, Denver forward Kenneth Faried was in a neck brace and strapped to a stretcher as he was wheeled off the court.
Faried, who took an elbow to the back of the neck while jostling for a rebound late in overtime, raised his arm for a thumbs-up to fans who stuck around.
"Obviously, any time you're dealing with a neck or back, it's scary," Nuggets guard Jameer Nelson said. "I didn't see the play. We were playing. There are no dirty guys out there. Nobody did anything intentional. Hopefully he's good."
The Nuggets said Faried was taken to the hospital for precautionary reasons while the team flew home to prepare for a game Sunday against Portland. A team spokesman said general manager Tim Connelly accompanied Faried to the hospital.
"You don't want to see that with anybody, with any player in this league," Denver forward Danilo Gallinari said.
Faried had 15 points and 12 rebounds in nearly 29 minutes for the Nuggets, who lost their fifth straight.
Curry came back following a two-game absence because of a bruised lower left leg but hurt it again in the same place when he got kicked in the leg playing defence. He didn't play the entire second half.
The star point guard finished with five points, four assists and two steals in 14-plus minutes. He will be re-evaluated Sunday to determine his status for Monday night's home game against Charlotte.
"I just re-injured the same thing, so I'll be all right," Curry said. "I know exactly what it is. Whenever you hurt something and you try to play through a little bit of discomfort and just get out there, it's usually a magnet for something to happen."
Will Barton, whose two shots late in regulation forced the extra period, missed an off-balance attempt following Thompson's go-ahead basket. Thompson then made one of two free throws before Barton's desperation 3-pointer at the buzzer hit the rim.
Barton dunked with 34.5 seconds left in the fourth quarter and with 0.9 on the clock as the Nuggets rallied to force OT.
The Warriors had just seven players available for overtime. They blew a 26-point lead before hanging on for their 34th straight regular-season win at Oracle Arena, including a franchise-best start of 16-0 this season.
Golden State (31-2) beat Denver for the fourth straight time overall and at Oracle Arena.
Thompson scored 26 points on 11-for-27 shooting. Green's 18 first-quarter points were a career best for a single period.
Gallinari returned to the Denver lineup and scored 24 points after sitting out six games with a sprained left ankle.
Warriors coach Steve Kerr told interim coach Luke Walton on Saturday morning he wasn't quite ready to be back on the bench, even after taking the last road trip with the team. Kerr is still recovering from complications such as headaches following two back surgeries.
"I know he wants to, and it's frustrating because it's out of his control," Walton said. "When that day will be, I have no idea. I don't think he knows, so we just keep going at it 'til he gives us the nod that he'll be back out there. He looked good on the trip. It was great having him out there. Hopefully that means he's getting closer."
Nuggets centre Jusef Nurkic made his season debut after undergoing left knee surgery in the off-season to repair his patellar tendon. The 7-footer went 0 for 5 from the field and scored three points in 5 minutes.
"We will try to acclimate him back in slowly but surely and he is going to give us a low-post presence I think will be a great addition for us," coach Michael Malone said.
Nuggets: PG Emmanuel Mudiay, who missed his 11th straight game as he recovers from a sprained right ankle, could be back within five to seven days to take pressure off Nelson, a 12-year veteran. "We've got to constantly check the treads on his tires," Malone said.
Warriors: NBA Finals MVP Andre Iguodala earned his first start since Game 6 of the Finals against Cleveland and first in the regular season since April 13, 2014, at Portland. ... G/F Brandon Rush missed the game with right hamstring tightness, and C Festus Ezeli sat out his third game in a row with a sore left toe. Joked Walton: "I told 'em I can give 'em 4 good minutes tonight." ... Golden State used its eighth different starting lineup. ... F Harrison Barnes hasn't played since Nov. 27 because of a sprained left ankle. "He's doing more and more," Walton said. "Would expect to see him back pretty soon." ... While Curry typically plays the entire first quarter, he rested for 3 minutes, 40 seconds.
Nuggets: Host Portland on Sunday.
Warriors: Host Charlotte on Monday.