Altuve notched an infield hit to lead off the frame against Jim Henderson (0-1) and the Astros then loaded the based with walks issued to Marwin Gonzalez and Steve Pearce.
Moore followed by lifting a flair hit to shallow left field, knocking in the game-winning run as Houston clinched its three-game set.
Pearce finished 3-for-4 with three RBI and Tyler Greene homered for the Astros, who also won in walk-off fashion in Friday's series opener.
Wilton Lopez (5-1) earned the victory despite allowing Jean Segura's game-tying RBI groundout in the ninth.
Norichika Aoki delivered a two-run double for Milwaukee, which dropped its 11th straight road game.