Golden State bounced back from a loss to Oklahoma City on Friday night that snapped an eight-game winning streak.
The Warriors led by five at halftime and used a 38-point third quarter, with 15 points from Curry, to take a 22-point lead into the fourth quarter.
The Rockets got five straight points from Kostas Papanikolaou to cut the lead to 110-94 with seven minutes left, but Golden State scored nine quick points after that, led by Curry's five, to make it 119-94 and cruise to the win.
It is Golden State's NBA-leading 24th double-digit victory and its third win over Houston this season. It's the first time the Warriors won a season series against the Rockets since 2006-07.
They finish the series on Wednesday at Golden State.
A 3-pointer by Josh Smith cut Golden State's lead to 10 with three minutes left in the third quarter. But the Warriors capped the quarter with a 12-0 run, with eight points from David Lee, to go up 102-80 entering the fourth quarter. Houston had four turnovers to help the Warriors build the lead.
Harden made just two of his first 12 shots and got his fourth foul on a charge with 1:44 left in the third. He was 4 of 15, including 0 of 4 on 3s, to finish well below his average of 27 points a game.
The Warriors scored the first five points and the second half to push the lead to 69-59. The Rockets used a 7-1 run, with four points from Howard, to get within 70-66 a couple minutes later.
Curry, who had 11 assists, got Golden State going again after that, making an off-balance layup as he was fouled. He tumbled backward and landed on top of a cameraman on the sideline before falling to the court.
He made the free throw and those three points were the start of a 10-2 run that extended the advantage to 80-68 midway through the third quarter.
The lead had changed 11 times and it had been tied 11 other times before Houston used a 7-0 run to make it 59-55 with about two minutes left in the first half. Smith started it when he grabbed a rebound down low and kicked it out to Trevor Ariza, who made a 3-pointer. Corey Brewer stole the ball and Smith finished with a reverse layup before another steal on the next possession led to a dunk by Ariza.
Golden State coach Steve Kerr called a 20-second timeout and the Warriors regrouped and finished the half with a 9-0 spurt to a take a 64-59 lead into halftime.
Warriors: Andre Iguodala got a technical foul in the second quarter. ... It's the first time Golden State has swept a road series against the Rockets since 1975-76.
Rockets: Howard received a technical with about 10 minutes left in the first quarter for arguing an offensive foul. ... Golden State's 64 first-half points were the second-most Houston has allowed before halftime this season. ... Golden State's 38 points in the third were the most the Rockets have allowed in a quarter this season.
Warriors: Host Nuggets Monday.
Rockets: Host Pacers Monday.