Next, they'll try to beat the Dallas Mavericks on Wednesday night for the first time in eight trips to the American Airlines Center.
Harden, the Rockets' leading scorer with 23.7 points per game, sat out Tuesday's 97-90 win over the Spurs with a bruised thumb, and coach Kevin McHale didn't have an update after the game on his status against the Mavericks (26-20).
Houston (30-17) improved to 5-2 without him this season, but one of those losses came against Dallas - a 111-104 home defeat on Dec. 23.
The Rockets and Mavericks split two meetings before that, with Dallas also winning 123-120 at home on Nov. 20 behind 37 points from Monta Ellis and 35 from Dirk Nowitzki. Houston blew a 14-point fourth-quarter lead in that one, its seventh straight road loss in the series.
Against San Antonio on Tuesday, the Rockets got 23 points and 16 rebounds from Dwight Howard while Terrence Jones added 21. Jeremy Lin started in place of Harden and chipped in 18 and eight assists as the Rockets went with a two-point-guard lineup with Patrick Beverley.
"We just kept grinding it out,'' said McHale, whose team improved to 3-0 against the Spurs this season. "We changed a couple of things defensively and the guys kind of dug in and got stops."
The win came after consecutive losses to Memphis in which Harden averaged 13.0 points on 33.3 percent shooting and sustained the injury in the second game - a 99-81 loss on Saturday in Memphis.
The Rockets have been held under 100 points in three straight games for the first time this season, shooting 40.4 percent and averaging 88.3 points - 16.5 under their season average. Against the Spurs, they managed to weather that with a 55-39 rebounding advantage.
"We missed a lot of shots, and they came out and hit some," Howard told the team's official website. "That's going to happen some nights, but we didn't give up. We kept fighting, we hit the offensive glass, Terrence got hot for a little bit and we just kept playing."
The Mavericks are looking to improve to 2-0 on a four-game homestand, and their leading scorer is also ailing. Nowitzki played through a sore left knee and scored 28 points Sunday in a 116-106 win over Detroit.
Ellis was held to 11 points and has turned the ball over 18 times in the last three games, but the Mavericks have been getting consistent guard play elsewhere. Devin Harris, just five games into a return from offseason toe surgery, played a season-high 24 minutes against Detroit and scored 14 points for a second straight game.
"On a night when Monta couldn't get it going, it's a godsend to have a guy like Devin available," coach Rick Carlisle said. "He's an experienced NBA player who's really done everything."
Harris has 16 assists and one turnover since returning.
"I'm making the most of my experience on the floor, trying to get used to playing with different guys in different situations," Harris said. "I'm using this as kind of my training camp."
Starting point guard Jose Calderon scored 17 against the Pistons on 7-of-8 shooting.