The Rockets were coming off a 90-88 win over New Orleans in which they tied a franchise record with only seven points in the final quarter. They outscored the Spurs 28-27 in the fourth on Saturday, shooting 59 percent from the field (10 for 17).
"It was definitely great to get over that hump," Lowry said.
Tony Parker had 24 points and a season-high 13 assists for the Spurs, who were playing their fourth game in five nights. San Antonio coach Gregg Popovich rested Duncan, who played 25 minutes in Friday night's loss to Sacramento. Tiago Splitter had a career-high 25 points and 10 rebounds for the Spurs, who dropped to 1-6 on the road.
San Antonio trailed 101-99 with a minute left. The Rockets nearly lost the ball in the backcourt, but Dragic picked it up and just beat the shot clock with a one-hander to put Houston up by four.
Richard Jefferson sank a 3-pointer with 11 seconds left, but Martin made two free throws to put it away for the Rockets.
"Some days, there are no excuses. They made plays at the end of the game," Jefferson said. "Tony had a great game, Tiago had a great game, two teams were battling back and forth. They made the right plays, we had a shot to tie it, and we don't get it done. Simple enough."
The Rockets shot 56 percent (44 of 79) to make up for the Spurs' 43-32 edge in rebounds.
"This was a tough one," Splitter said. "We did a good job, but they hit unbelievable shots at the end."
Houston opened the game with a 9-0 run after the Spurs missed their first four shots and coughed up three turnovers in the first 2½ minutes.
The Rockets continued to shoot well in the second quarter, but the Spurs began scoring inside to stay close. Parker turned a steal into a fast-break layup, then hit a driving one-hander to tie it 41-all.
Dalembert dunked with a minute left in the half, and Houston led 55-49 at the break. Parker had 13 points and seven assists in the first half.
"Tony was kind of in the one-man-game thing, going mid-screen," Houston coach Kevin McHale said. "He was just making plays."
Matt Bonner and Jefferson opened the second half with 3-pointers to tie it again. Martin then scored the next seven points, finishing the burst with his second 3-pointer.
With Parker on the bench for much of the third quarter, the Spurs rallied again and Splitter's layup cut the deficit to 72-71. Parker returned with 2:21 left in the quarter, and his long jumper just before the quarter buzzer drew the Spurs to 77-75.
Parker then came out of the game and did knee bends behind the bench, with a towel and a heating pad pressed against his left hip. San Antonio led 84-83 when he returned with 7:39 remaining.
"We believe we can win with whatever lineup we put out there," Bonner said.
Lowry's 3-pointer with 3:07 left put Houston up 99-92. The Rockets went 0 for 8 from 3-point range in Thursday's win over New Orleans.
"We made shots," Lowry said. "We tried to push the tempo a little bit and use our speed and quickness to our advantage."
Bonner hit a 3 and Gary Neal made a running shot to quickly get the Spurs back in it. But Dragic ended up with the ball after a scramble and hit a mid-range jumper.
"Guys were making plays," Martin said. "Kyle played great, Goran played great and then defensively, we were at our best, once again. It was a grind-it-out game."
The Spurs are 1-3 starting their stretch of 16 of 21 games on the road. ... Splitter recorded his second double-double. ... Parker was four assists shy of his career high, set last season. ... The Rockets have held double-digit leads in nine straight games, tying the longest streak since 2008-09. ... The teams were playing for the third time this season, and wrap up their four-game season series in San Antonio on Feb. 1.