Jose Abreu and Chas McCormick knocked in two runs apiece and Jose Altuve scored three runs.
Detroit native Hunter Brown (10-9) was the winning pitcher. He allowed two runs, four hits and two walks in five innings while posting nine strikeouts.
Tigers starter Eduardo Rodriguez (9-7) was charged with four runs and five hits in 4 2/3 innings. He also walked four batters and struck out one.
Parker Meadows, who hit a game-winning, three-run homer on Friday, had two hits and an RBI for Detroit.
The Astros took the lead two batters into the contest. Altuve reached on an infield single and scored on Bregman's double to center. Houston had runners at the corners with two outs but Rodriguez induced Yainer Diaz to pop out.
Detroit had a threat going in the bottom of the inning as Riley Greene doubled and Spencer Torkelson walked. Brown then struck out the next two batters.
Houston had the bases loaded with two out in the second. Rodriguez escaped that jam by getting Yordan Alvarez to pop out.
Detroit evened things up in the fourth. Kerry Carpenter hit a one-out single, stole second and scored on Meadows' single to right.
Houston took a 4-1 lead in the fifth. Altuve drew a leadoff walk and Bregman followed with his 21st homer, a shot to left.
The Astros had two runners on with two out and Rodriguez was taken out in favor of Will Vest. Abreu slapped a single to right to knock in Kyle Tucker.
Detroit got one of those runs back in the bottom of the inning. Zach McKinstry walked, moved to third on a Carson Kelly single and scored on Greene's sacrifice fly.
The Astros made it 6-2 in the sixth. Bregman doubled to knock in Altuve, who also doubled. Bregman scored on an Alvarez single.
McCormick's two-run single and another Abreu RBI single off Jose Cisnero increased the Astros' advantage to seven.
—Field Level Media