The Rockets were 22 for 50 on 3-pointers, the most 3s attempted and made against the Spurs in their long postseason history.
Houston had six players in double figures, including 20 points and 13 rebounds from Clint Capela.
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Game 2 is Wednesday in San Antonio.
Houston led by as many as 39 points, including a 30-point lead in the first half, in the opener of the first series between the rivals since the Rockets' victory in the 1995 Western Conference finals.
While the hot shooting wasn't completely unexpected from the explosive Rockets, the defense was. Houston was active in rotating to San Antonio's shooters and had both defenders stay on Kawhi Leonard on screens.
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Leonard had 21 points, fighting his way to 5-for-14 shooting.
Tony Parker added 11 points and Jonathon Simmons had 10 for the Spurs.
Houston led 69-39 lead in the first half, the Spurs' largest halftime deficit under Popovich.
Popovich called a timeout 80 seconds into the game, berating David Lee for a missed defensive assignment that led to a 3-pointer.
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It didn't help.
Houston hit 12 3-pointers in the first half, the most San Antonio has allowed to a playoff opponent in the opening two quarters.
The game got testy in the second half with a pair of ejections.
Nene was thrown out at the close of the third quarter after grabbing Dewayne Dedmon by the throat after the Spurs center and Harden got in each other's face. Dedmon was thrown out in the fourth quarter after arguing with officials during a free throw.
Rockets: Houston owns an 11-6 postseason record against San Antonio, winning all three previous playoff series against the Spurs. . The Rockets have won six straight postseason games in San Antonio. Houston's last postseason loss in San Antonio was May 30, 1995. . Rockets owner Les Alexander bought tickets to Game 1 for about 150 staff members, family and friends, bringing the group in several buses from Houston to the AT&T Center. . Rockets center Chinanu Onuaku, who is on assignment with Rio Grande Valley, was suspended two games without pay for pushing an official during a Development League playoff game on Thursday.
Spurs: San Antonio's largest postseason defeat under Popovich was a 111-72 defeat to the Lakers on May 25, 2001, in Game 3 of a four-game sweep in the West finals. . Leonard has scored in double figures in 27 straight playoff games. . Danny Green has 169 career 3-pointers in the postseason, moving past former Spurs forward Bruce Bowen for 24th in league history. . Patty Mills has made at least two 3-pointers in 24 postseason games, second most in franchise history to Manu Ginobili's 62.
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