Curry, however, settled the nerves by making two free throws to seal things for Golden State, who got 18 points off the bench from Shaun Livingston.
"Game One slipped away from us," Harden said after Trevor Ariza scored 20 points and Josh Smith added 17 and seven rebounds for the Rockets.
"We had several opportunities to win the game.
"We have to look at the film and correct things and be better in Game Two."
Houston center Dwight Howard suffered a knee injury in the first quarter, returned for a while but left for good in the fourth and they will need his inside presence as the series progresses.
"He's our top rebounder and protects the paint," Houston coach Kevin McHale said of Howard. "Hopefully he'll be better."