Harden, who leads the league with an average of 36.6 points per game, was ruled out by illness but the Warriors were powerless as they lost their first home game in six.
Steph Curry had 25 on the night and brought Golden State to within four points with around a minute left to play, before Paul made a pair of free throws to put the game on ice.
LeBron James had 27 points and 12 assists, but his Los Angeles Lakers went down 128-115 to the New Orleans Pelicans.
Jrue Holiday scored 27 for the Pelicans, while former Laker Julius Randle added 24.
The Portland Trail Blazers had a 130-115 win over the Philadelphia 76ers with Jusuf Nurkic scoring 24, while the Atlanta Hawks edged out the Phoenix Suns 120-112.
— Brooklyn Nets (@BrooklynNets) February 24, 2019
D'Angelo Russell had 40 points as the Brooklyn Nets saw off the Charlotte Hornets 117-115, the Cleveland Cavaliers beat the Memphis Grizzlies 112-107 and the Indiana Pacers ran out 119-112 winners over the Washington Wizards.
Kyrie Irving hit 37 points and had 10 assists but his Boston Celtics went down 126-116 to the Chicago Bulls, the Detroit Pistons beat the Miami Heat 119-96 and Russell Westbrook had 41 but the Oklahoma City Thunder lost 119-116 to the Sacramento Kings.
Giannis Antetokounmpo had 27 points and 10 rebounds as the Milwaukee Bucks beat the Minnesota Timberwolves 140-128 and the Utah Jazz won their first game in three 125-109 against the Dallas Mavericks.