The doubleheader was scheduled after the Athletics and Astros decided not to play Friday night in order to raise awareness of racial inequality in the wake of the police shooting of 29-year-old Jacob Blake, a Black man, in Wisconsin.
Houston won for the fourth time in five games and cut Oakland's lead in the AL West to 2 1/2 games.
Tucker's major league-leading sixth triple gave the Astros a 3-1 lead in the first.
"I've been seeing the ball real well," Tucker said. "I haven't chased a lot of pitches. ... If you're not chasing pitches, and you're getting pitches over the plate to hit, you'd be more productive that way."
Tucker is batting .357 (20 for 56) with five homers and 20 RBI in his last 17 games.
"You know it was in there," Houston manager Dusty Baker said. "You just have to get some hits. He's using the whole field. He's staying off tough pitches. That's the main thing. ... He's confident; he's calm. He's getting his pitch to hit and isn't missing."
Springer increased Houston's lead to 5-1 with a two-run shot off Frankie Montas (2-3) in the second. Springer had two hits in the second game. He returned to the lineup Saturday after sitting out Tuesday's doubleheader with a bruised left elbow.
"I felt like mostly everything was just location, I was missing my spots a lot," Montas said. "They're a good team and they're really good when you make mistakes."
Laureano opened the game with his second career leadoff homer. Chapman, who drove in both of Oakland's runs in the first game, connected in the fourth against Zack Greinke (2-0).
Tommy La Stella, who was acquired in a trade with the Angels on Friday, cut Houston's lead to 5-3 with a run-scoring groundout in the fifth.
"It wasn't our best game, I don't think he had anything to do with that," Oakland manager Bob Melvin said of La Stella. "It's a team game. We've seen enough of him to know he's a good hitter and a good player. Just overall we didn't play a good game today."
Greinke allowed six hits and struck out six in five innings. Greinke has given up three runs or fewer in each of his seven starts this season.
Baker said Greinke had a "crick" in his neck, so he had Cy Sneed warming up with Greinke as a precaution. Greinke said his neck loosened before the game.
"It was a tough game," Greinke said. "The defense did great, and I got run support."
McCullers (3-2) allowed two runs -- one earned -- and six hits in the first game.
"I was really happy with the changeup today," McCullers said. "And my breaking ball and really most of my stuff. I made a little adjustment midweek. I threw two bullpens this week with the hurricane days, and I made a little adjustment with my front side. It felt like it was coming out more consistent on that two-seam line."
Tucker put Houston ahead to stay in the first game with his sixth homer in the first inning, a drive off Chris Bassitt (2-2) that went just inside the right-field foul pole.
DOUBLEHEADERS IN HOUSTON
Saturday's doubleheader was the second for the Astros this week and third in Minute Maid Park history, with the other one on Sept. 2, 2017, against the Mets following Hurricane Harvey. The Astros and Angels moved up Thursday's game to Tuesday ahead of Hurricane Laura, which made landfall in Louisiana on Thursday morning. Houston's game on Wednesday against the Angels was postponed.
LA STELLA ARRIVES
La Stella said he took an early flight from California to Houston and got in about an hour before the first pitch of the first game. He didn't play in the opener and went hitless in the second game.
Astros: INF Aledmys Diaz was reinstated from the 10-day injured list.
Athletics: LHP Jesus Luzardo (2-1, 3.74 ERA) will make his sixth start of the season Sunday in the series finale. He is coming off his first loss after allowing three runs in 6 2/3 innings against the Rangers.
Astros: LHP Framber Valdez (3-2, 2.35 ERA) is scheduled to start on Sunday. Valdez has won three straight starts.