Stephen Curry added 18 points, six rebounds and eight assists for the Warriors, who were outclassed early but battled back to seize the lead in the best-of-seven Western Conference final, which continues in Houston on Wednesday, AFP reported.
"It's a great start. We played well," said Thompson, who scored 11 points in the fourth quarter.
"It's nice to be at home but we've got a lot of guys who have been in this league a long time. We've been in every situation".
Either the Warriors, seeking their third crown in four seasons, or the Rockets, who had the best record in the NBA this season, will face Cleveland or Boston in the NBA Finals.
"If we're going to knock these guys off we have to get a better mental focus," Rockets coach Mike D'Antoni said. "We ran out of gas a little bit in different spots and they didn't.
"It's just a bunch of stuff we can clean up and we will. We'll come out and attack them Wednesday."
Durant, who scored 17 first-half points, sparked the Warriors after the Rockets attacked early but were overtaken in the second quarter.
"You know they are going to come out with a lot of energy," Durant said. "We just tried to take their best punch and keep fighting".
NBA scoring champion James Harden scored a game-high 41 points to lead the Rockets while Chris Paul added 23 points and 11 rebounds.
"We know James is always going to score over us. We just had to keep solid and keep playing hard," Durant said.
"This Houston team never stops. They are always in the game with three-point shots. We play a calm steady game, look for a good shot and play good D every time down.
"I just try to be aggressive and look for a shot every time I go down."
The Warriors appeared to lose the ball in the back court after a long rebound, but no violation was called and Thompson sank a three-pointer seconds later for a 106-96 edge with 3:55 to play, all-but sealing Houston's fate.
The Rockets jumped ahead 9-2 and 21-12 but the Warriors battled back, taking their first lead of the game at 35-33 on David West's layup 2:57 into the second quarter.
Harden scored the last of his 24 first-half points on a fast-break dunk but Golden State's Nick Young answered with his third three-pointer of the half to lift the Warriors level 56-56 at halftime.
"They took the challenge and played awfully well," Warriors coach Steve Kerr said.