HOUSTON -- From coach Gregg Popovich through a decent sample of players in the locker room, the San Antonio Spurs were quick to attribute a measure of good fortune to being in position to rely on their renowned execution with the game on the line.

Reserve guard Patty Mills drilled an open 3-pointer with 12.9 seconds remaining and the Spurs erased a 13-point, fourth-quarter deficit en route to a 102-100 victory over the Houston Rockets on Tuesday night at Toyota Center.

The Spurs (23-5) extended their winning streak to five games with a 19-4 game-ending run, a rally that included five 3-pointers inside the final 4:18.

With San Antonio trailing 100-99, Mills received a pass from Manu Ginobili before calmly sinking the decisive trey.

"I have no clue (how I got open)," Mills said. "I didn't do anything other than just stand there. It was a hell of a pass.

"It was a broken play. It was what we work on all the time, driving and kicking. Manu did a great job of getting into the lane."

While Houston (21-8) fueled the Spurs' comeback with eight fourth-quarter turnovers, the outcome was essentially decided by 3-point proficiency. Mills and Ginobili combined for 25 points off the bench, hitting 7 of 11 3-pointers. The Spurs finished 12 for 23 from behind the arc. Conversely, the Rockets weren't as sharp.

Houston had its 10-game winning streak snapped by missing 32 of 38 3-pointers, including a wide-open look from guard Eric Gordon (13 points) following the Mills basket. The Rockets' streak of games with at least 10 3-pointers made ended at 27.

"We just turned the ball over and didn't make shots," Rockets guard James Harden said. "Simple."

Harden posted 31 points, 10 rebounds and seven assists but missed 10 of 11 3-point attempts. Gordon missed 7 of 8 from behind the arc, while forwards Trevor Ariza (16 points, six boards, four steals) and Ryan Anderson finished a combined 4 of 12 on treys. Guard Patrick Beverley missed all four of his attempts from deep.

The final period featured wild swings of momentum. Houston answered an 8-0 spurt by the Spurs with an 8-0 run, six points at the free-throw line, to reclaim a seven-point lead. That was part of a larger 17-3 push that upped the lead to 96-83, but the Spurs responded immediately with an 11-0 blitz to close the deficit to two.

The Rockets appeared to steady themselves with a Harden layup and an Ariza basket in transition, but the hosts' turnovers undermined their defensive intensity.

"I know the biggest thing that happened is that we had about three or four wide-open shots we missed," Rockets coach Mike D'Antoni said. "They had three or four wide-open shots, and they hit them."

The Spurs' inability to take full advantage of the Rockets' cold start from the perimeter proved instrumental in the Houston comeback. While LaMarcus Aldridge (17 points, 10 rebounds) and Kawhi Leonard (21 points, five steals) were effective early, the Spurs couldn't generate the complementary offense to punish the Rockets.

Houston started 0 of 14 from behind the arc and didn't record its first 3-pointer until Ariza sank a corner shot with 4:04 left in the first half. Harden and Gordon added treys in succession, and after trailing by as many as 10 points earlier in the half, Houston sliced that deficit to 44-43 with three minutes left in the second period.

The Spurs extended the lead to seven by the break, but the tone was set for the Rockets to keep clawing on both ends despite their wayward shooting from deep. Yet despite their best effort, they missed too many shots to find a path to victory.

"We got a break because they shot terribly," Ginobili said. "We did a pretty good job of contesting many of them, but they shot (and missed) some open ones, too, and that's not what they usually do."

NOTES: Rockets C Clint Capela will miss at least four weeks after sustaining a small left fibula fracture Saturday night against the Minnesota Timberwolves. Capela, averaging 11.8 points, 8 rebounds and 1.6 blocks per game, will be re-evaluated in four weeks. Houston started veteran Nene at center and could use F Ryan Anderson there as well. ... The Spurs featured their full complement of players. In the previous meeting between the teams on Nov. 12 in Houston, the starting backcourt of Tony Parker and Danny Green were together for the first time. ... The Rockets recalled C Chinanu Onuaku from their NBA D-league partner, Rio Grande Valley. Onuaku ranked third in the D-league with an average of 10.3 rebounds over 16 games with the Vipers. He also ranked fifth in shooting from the floor at 62.8 percent.