Curry scored 14 of his 27 points in the third period as the Warriors secured their fourth consecutive berth in the NBA Finals.
"This is a situation we've never been in before ... to win a Game 7 on the road, keep our composure for the whole series," Curry said postgame on TNT. "All those hurdles and obstacles, we got over them, so it's an unbelievable feeling, man. Winning a championship is hard, so this is a testament to that."
The championship series begins on Thursday in Oakland, Calif., with the Cleveland Cavaliers representing the Eastern Conference. The same two teams met in the previous three Finals, with Golden State winning the title in 2015 and 2017 and Cleveland emerging as the champ in 2016.
Golden State, after trailing by 11 points at the intermission, outscored the Rockets 33-15 in the third period. The Warriors posted a plus-68 scoring margin in the third quarters for the series.
"The second half was unbelievable," Curry said. "This atmosphere is crazy."
The Rockets fashioned their halftime lead on effort, both defensively and on the glass, but when their offense collapsed in the third quarter, their verve dissipated. Houston shot 24 percent (6 of 25) in the third and while missing all 14 of its 3-point attempts. Curry, meanwhile, finished the frame 5 of 6 from the floor while draining 4 of 5 from beyond the arc as the Warriors shot their way to the lead.
Warriors coach Steve Kerr said, "I'm proud of our guys for the way they held together after almost coming completely unglued in the first half. But that second half was something, a lot of amazing shot-making from some talented players. And I don't know what the hell else was going on out there, but we did fight and we got it going in the second half."
The Rockets missed 27 consecutive 3-point attempts -- an NBA playoff record -- before PJ Tucker drilled a corner trey with 6:28 left that cut the deficit to 10 points. Houston went 7 of 44 from deep, 15.9 percent, while Golden State made 16 of 39 3-point attempts, 41 percent.
Kevin Durant totaled 34 points, five rebounds, and five assists for the Warriors, and Klay Thompson chipped in 19 points despite early foul trouble. Curry also produced nine boards, 10 assists and four steals.
James Harden posted 32 points, six rebounds, six assists and four steals for the Rockets, who again were without guard Chris Paul (right hamstring strain).
Rockets guard Eric Gordon, who scored 23 points, said of the impact of Paul's absence, "It sucks because you know you could win this series if we just had one more playmaker. If we had Chris, if he was out there, we'd have been playing on Thursday. It's just tough."
Harden had a different viewpoint.
"We don't even think about that," Harden said of playing without Paul. "We had an opportunity tonight and last game without Chris. Obviously, he's a big part of why we're here, but we had opportunities, especially in that first half both games."
Harden opened the game 4 of 5 from the floor but finished 12 of 29 for the game. Gordon shot 2 of 12 from 3-point range, slightly better than Harden's 2 of 13.
While Clint Capela (20 points, nine rebounds) and Tucker (14 points, 12 rebounds) delivered on the interior, the Rockets were undone by their ineffective perimeter options. Trevor Ariza finished 0 of 12, including 0 of 9 on 3-point tries, while Gerald Green made just 1 of 7 shots.
Harden, who gave the Rockets a 48-33 lead with a transition dunk at the 4:54 mark of the second quarter, fed Capela for an alley-oop layup for a 61-55 lead with 5:38 left in the third. The Warriors followed with a 17-2 run that included five 3-pointers, four from Curry, whose finger-roll with 3:29 left in the period was the lone basket from inside the arc during the decisive run.
"First of all, they've done that all year against everybody," Rockets coach Mike D'Antoni said of the Warriors' third-quarter surge. "That's what their trademark is; we know it and it's not like it's a secret. Just seems like they came out a little more determined than we were in the beginning. The juice was flowing on their side. When they get it going, it's tough to turn them off."
Durant praised the Rockets, who fell short in the playoffs after posting a league-high 65 wins in the regular season.
"Much respect to the Houston Rockets for bringing the best out of us and making this an incredible series and pushing us to the brink," Durant said. "You've got to give respect to them and the great season that they had. But I'm glad that we're going back (to the Finals) and I'm excited that we've got this opportunity. I look forward to taking advantage of it."
--Field Level MediaBet Now