"It was by far his best outing of the season," Houston manager Cecil Cooper said. "He attacked the hitters. Those guys as aggressive as they are, you've got to attack them."
The right-hander allowed three runs and five hits over 6 1/3 innings. Backe struck out five and didn't walk a batter for the first time in 10 starts.
This was only the second time Backe has pitched into the seventh this season.
"No walks are definitely a good deal," Backe said. "It keeps the pitch count down. It's been rare for me to get into the seventh inning this year so that helped out a lot."
Texas, who won the first two games of the series by a combined 22-10, couldn't complete a sweep of its in-state rival. The Rangers have won their last seven series for the first time since 1999.
"We're playing good baseball and that's all you want to do," Texas manager Ron Washington said. "It's not easy to sweep someone."
Lance Berkman was 2-of-5 to keep his average at .399. He has a 17-game hitting streak in which he is 36-of-66 with eight home runs and 21 RBI.
Berkman was in a joking mood after the game. When asked about Houston finishing 7-3 on this road trip, Berkman replied, "It's a miracle."
Brandon Backe is amazed by Berkman's hot run.
"I'm sure he's dumbfounded by what he's doing himself," Backe said. "It seems like everything is falling right now. We need to ride that train as long as possible."
Cooper was thrown out in the sixth inning by umpire Angel Campos, the second time he's been tossed in three games. He came out to argue when Michael Bourn was thrown out trying to steal second base.
Campos also tossed Cooper when he argued a close play at the plate Friday night.
"I'm sure he thought I was still upset or angry about the other night," Cooper said. "But I just wanted to find out what he saw there."
Kason Gabbard (1-1) allowed five runs and nine hits in five innings for the Rangers.
Gabbard held the Astros to only one hit through the first three innings before they opened the scoring in the fourth.
Tejada, Berkman and Hunter Pence -- who extended his hitting streak to 16 games -- singled to load the bases with one out. Mark Loretta walked to force home a run, Ty Wigginton had an RBI grounder and J.R. Towles added a run-scoring double to give the Astros a 3-0 advantage.
The Astros scored two more in the fifth on Tejada's RBI double and Carlos Lee's sacrifice fly.
Ian Kinsler and Catalanotto singled off Backe with nobody out in the fourth, and Michael Young popped up to Houston second baseman Kaz Matsui in shallow right. Kinsler tried to score on the play from third, but Matsui's throw to the plate beat Kinsler by several feet.
Backe struck out Bradley to end the threat.
Kinsler said he made the decision to sprint home on his own.
"I got a little too overaggressive," Kinsler said. "I was trying to make something happen."
The Rangers knocked Backe out of the game in the seventh. Bradley hit a two-run homer -- his eighth of the season -- and Murphy followed with his sixth.
Doug Brocail came out of the bullpen and got the final two outs of the seventh.
Texas outfielder Josh Hamilton, who leads the majors with 49 RBI, did not start Sunday after leaving Saturday night's game with soreness. Hamilton pinch hit and grounded out in the eighth before playing right field in the ninth.
- The Rangers finished their nine-game homestand 6-3.
- Towles snapped a 1-of-18 slump with his RBI double.
- Matt Harrison threw a seven-inning no-hitter for Texas' Double-A affiliate Frisco in the first game of a doubleheader against San Antonio on Sunday.