Houston remains two games back of the AL's second Wild Card spot.
"It's a big win for us to come into this place and beat a first-place team, so regardless of how they lined their pitching up, you've got to win as many games as you can," Astros manager A.J. Hinch said. "That was the lovable September marathon that we all enjoy. Better to be on the winning side than the losing side, but that one seemed like it was never going to end."
Bregman's two-run blast in the third, combined with an RBI double from Jose Altuve in the first and a three-run outburst in the seventh, helped back an effective outing by Houston right-hander Mike Fiers.