Four-time NBA champion Curry made 22 of 38 shots from the floor, 10 of 23 from three-point range, and added six rebounds and four assists for the injury-hit Warriors.
"Steph was incredible," Warriors coach Steve Kerr said. "What a performance. I just feel so bad for him and for our guys because they are battling, Steph was sublime."
Curry was one shy of matching the NBA record for three-point attempts in a game and the 35-year-old guard joined the late Kobe Bryant as the only players over 35 to score 60 or more in an NBA game.
In another key game, LeBron James scored 24 points and Austin Reaves added 22 to lead the Los Angeles Lakers to a 113-105 victory at New York, snapping the Knicks' nine-game win streak.
The Lakers outscored New York 33-19 in the fourth quarter to spoil a 36-point performance by Jalen Brunson.
"We just turned up our defensive intensity," James said of the late heroics. "We was really on point and on time with our doubles, with our hits, with our rotations.
"Jalen is playing at more than an All-Star level this year, so we know he's the head of the snake. We just tried to wear him down in the fourth quarter, keep him on multiple bodies, keep changing up defences and I think that helped out a lot."
In Atlanta, Curry scored 22 points in the fourth quarter and eight more in overtime and looked to have given Golden State the victory on a jumper for a 123-121 lead with 14 seconds remaining in regulation time.
But Murray answered from 14 feet with 4.1 seconds to play to force overtime, then scored seven consecutive points in the Hawks' 11-0 run to open the extra session and secure the triumph.
"I'm just glad our team got the win," Atlanta guard Trae Young said. "Steph was going in that second half. He got up to 50, wherever he was going, and in overtime we got a few more stops, got some rebounds and made a few more plays."
Curry, whose career high is 62 points from a January 2021 win at Portland, took off his jersey after the game, autographed it and gave it to actress Lindsay Lohan.
Young led Atlanta with 35 points while Murray finished with 19 points. Jalen Johnson had 21 points and 13 rebounds while Onyeka Okongwu had 22 points and 16 rebounds off the bench.
Young praised Murray's clutch effort down the stretch.
"That's what we need from him," Young said of Murray. "We need him to be aggressive. He brings a lot to our team. He has a lot of talent. We can't win without him scoring and getting everybody involved."
Giannis hits 48
Giannis Antetokounmpo scored 48 points to power the Milwaukee Bucks over hosts Dallas 129-117.
Damian Lillard added 30 points for Milwaukee while Luka Doncic had 40 points, 11 assists and nine rebounds in a losing cause.
Milwaukee's victory secured the Eastern Conference All-Star coaching spot for Bucks coach Doc Rivers, who replaced Adrian Griffin as the team's coach only eight days ago.
Boston head coach Joe Mazzulla, whose Celtics have a better record, is not eligible for the All-Star spot because he had the job last season.
The Philadelphia 76ers, playing without reigning NBA Most Valuable Player Joel Embiid due to a right knee injury, suffered their fifth loss in six games, falling 136-121 at home to the Brooklyn Nets.
Cam Thomas scored 40 points to lead Brooklyn, who also got 23 points from Mikal Bridges.
Sacramento's De'Aaron Fox scored 41 points to lead the Kings over hosts Chicago 123-115.
Domantas Sabonis had a triple-double with 13 points, 14 rebounds and 10 assists for Sacramento while Malik Monk added 22 off the bench.
Cleveland's Donovan Mitchell scored 31 points while Evan Mobley added 28 to spark the Cavaliers' 117-101 triumph at San Antonio.
French rookie star Victor Wembanyama scored 19 points and grabbed 14 rebounds for the Spurs.
