The reigning MVP scored 43 points, 10 rebounds and 12 assists as the Rockets ran riot from the start, surging to a 28-point lead in the first half.
On the way to victory, Harden hit 30 points before the beginning of the third quarter, made eight three-pointers and finished with his sixth triple-double of the season.
Ante Zizic top scored for Cleveland with 18 points but his side's torrid run continued as they fell to their 12th loss in a row.
Curry scored five at Oracle Arena to reach 2,285 and now trails Reggie Miller on 2,560 and Ray Allen on 2,973.
It was also a monster night for Klay Thompson, who scored seven three-pointers and 30 points overall to lead his side to the 146-109 win.
In Washington, Tomas Satoransky had his first career triple-double to help push the Wizards 113-106 past the Milwaukee Bucks.
The Wizards matched their franchise record of 18 three-pointers and led for most of the night as the Bucks struggled with the absence of Giannis Antetokounmpo, who was ruled out with a hip and quad injury.
The Atlanta Hawks edged the Philadelphia 76ers 123-121 as Jimmy Butler missed two free throws and the chance to tie with 2.4 seconds left on the clock.
John Collins scored 25 points including a fadeaway jumper with 25 seconds remaining, while Kevin Huerter led the way with 29 points.
The Dallas Mavericks beat The Minnesota Timberwolves 119-115, Luka Doncic finishing with 29 points and the go-ahead three-pointer, while Domantas Sabonis matched a career-high 30 points as the Indiana Pacers overcame the New York Knicks 121-106.
In the night's other games, the Toronto Raptors topped the Brooklyn Nets 122-105 for a fourth straight win, and Utah Jazz's Donovan Mitchell outclassed the Los Angeles Lakers, scoring 33 points with nine assists in the 113-95 win, and the Portland Trail Blazers improved to six wins in seven games, downing the Charlotte Hornets 127-96.