Paul scored 33 points with 11 rebounds, Harden bested Stephen Curry twice in the final seconds and the Rockets held off the Warriors 116-108 to snap their 14-game road winning streak, The Associated Press reported.
The victory gives Houston a 2-1 series advantage over Golden State after the reigning NBA champions had won the series the previous three seasons.
"Obviously they're a championship caliber team for the past four years ... and that's what we're trying to build our way up to," Harden said.
Harden stepped back from Curry for a three-pointer as the shot clock expired to make it 114-108 with 1:10 left, then blocked Curry's three-point attempt after a timeout.
Harden finished with 22 points. Paul added two free throws with 28 seconds left.
Golden State lost away from home for the first time since November 22. The Warriors had won seven straight in Houston.
"It's been a good streak, disappointing end to it," coach Steve Kerr said. "But we didn't deserve to win tonight. We played pretty poorly, did a lot of things to hurt ourselves and we're playing a great team. Can't get away with it."
Houston coach Mike D'Antoni raved about the performance of the 32-year-old Paul.
"The guy is a winner, he's been a winner, he's going to win," D'Antoni said.
Kevin Durant led Golden State with 26 points, Draymond Green had 21 and Curry added 19 on a night he went 5 of 15 on three-point attempts and 6 of 20 overall. It was just the sixth time in his career that he'd attempted 20 or more shots while making six or fewer.
"It was just one of those nights where I personally didn't have the right vision on the floor," he said. "So I've got to take that responsibility for that one. It was pretty bad."
The Warriors were wrapping up a five-game road trip and had won the first four games to tie a franchise record for consecutive road wins. But they struggled from the outset Saturday and trailed by double digits for most of the first half.
It was Harden's second game back after missing seven with a strained hamstring. He was in a much better rhythm than in his return Thursday night, when he scored a season-low 10 points. He had eight assists, two steals and two blocks Saturday.
The Rockets got the victory despite missing Trevor Ariza and Gerald Green, who were both serving the second game of a two-game suspension for an altercation with the Clippers. Clint Capela added 18 points for Houston on a night when top reserve Eric Gordon went 0 for 9 from three-point range and finished with just six points.