After being down 13 points heading into the fourth quarter, the Rockets ratcheted their defense, holding the defending champs to just 20 points in the final frame.
Houston counted on key points from the bench, including contributions from newest Rockets, Luc Mbah a Moute and P.J. Tucker, as well as Eric Gordon. The bench combined to score 58 points.
James Harden contributed a game-high 27 points along with 10 assists. In his debut, Paul scored just four points but dished 11 assists.
Head coach Mike D'Antoni kept Paul on the bench down the stretch due to a sore knee.
Trevor Ariza sunk a three-pointer with 2:09 remaining in regulation to bring the Rockets within one point at 119-118. After a jumper from Golden State's Patrick McCaw, Houston scored on a layup from Harden and later free throws from Tucker to put Houston in the lead at 122-121 with under 45 seconds left.
With both teams trading missed possessions, the Warriors had the last chance at a game-winning basket. With under 12 seconds left, Golden State's Stephen Curry launched a three-point shot that missed.
The ball eventually got into the hands of Kevin Durant who appeared to have made the winning basket for the Warriors, but a review waved the shot off and secured Houston's victory.
The Rockets (1-0) have little time to celebrate spoiling the Warriors' championship banner and ring ceremony. Houston takes on the Kings in Sacramento on Wednesday night. Game time is scheduled for 9 p.m.
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