Altuve tied it at 2 in the sixth with an RBI double, and Tucker put Houston ahead with his single three batters later, chasing starter Luke Weaver (1-8). Tucker has driven in four in the last three games and has 41 RBI this season.
"The RBI are based on the guys being on base in front of me," Tucker said. "I just try to go up there and hit the ball hard and go from there."
Altuve also had a run-scoring groundout in the third. The three-time AL batting champion is hitting just .219 this season.
The Astros improved to 26-26 and remained in second place in the AL West.
"We just want to be there to get our best baseball ahead," manager Dusty Baker said. "Under a normal 162-game season, you wouldn't be that worried about Jose because you figured he had another 300 or 400 (at bats) to go.
"The only reason guys are concerned and pressing a little is because of the shortened season. Our best baseball is ahead of us."
Arizona's Kole Calhoun hit his sixth homer in five games, leading off the second inning with a solo shot to right. Calhoun has 15 homers this season.
Josh Rojas increased the lead to 2-0 in the third on a sacrifice fly.
Weaver allowed three runs and five hits with five strikeouts in 5 1/3 innings in losing his fifth straight decision.
"Obviously, the sixth inning wasn't what we wanted," Arizona manager Torey Lovullo said. "He made a few mistakes and they jumped on him for two runs and their bullpen held on. Overall, I thought Luke was fantastic."
Weaver said he didn't have crisp command, but he was making the pitches when he needed to.
"I was able to get some three ups and three downs, but in the sixth inning, I had a couple of tough blows there and just not really winning," Weaver said. "It was a very unfortunate inning to say the least."
Cristian Javier, who started for the first time in 12 days, allowed two runs and four hits with six strikeouts in four innings.
"I felt good," Javier said through a translator. "I felt healthy. I felt strong. There were a couple pitches that didn't land. They were outside the zone, not where I wanted them, but I was able to make the adjustments and have a good outing."
ARIZONA FINISHES MARTE TRADE
The Diamondbacks acquired LHP Julio Frias from Miami as the play-to-be-named to complete the Aug. 31 trade that sent OF Starling Marte to the Marlins.
Astros: RHP Justin Verlander said on Instagram that he would have Tommy John surgery. Verlander is expected to be out through the 2021 season. He went on the injured list after his July 24 start against the Mariners with a right forearm strain and attempted to come back this season, throwing to live batters on Wednesday, but the reigning AL Cy Young winner said "he felt something in (his) elbow" after throwing on Wednesday and opted for Tommy John after seeing the MRI and consulting with doctors.
Diamondbacks: LHP Madison Bumgarner (0-4, 8.53) starts Sunday, looking to rebound after allowing eight runs in 5 1/3 innings in his last start against the Angels on Tuesday.
Astros: RHP Jose Urquidy (1-1, 2.70) will make his fourth start of the season Sunday after allowing one run in seven innings in a win over the Rangers on Tuesday.
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