Keuchel (2-7) held the Phillies scoreless despite yielding four walks and five hits. The left-hander got the big outs when he needed them.
Maxwell's two-run blast in the first inning put Houston ahead to stay. Jose Altuve, Ben Wallace and J.D. Martinez added RBI for the winners.
Houston reached Kyle Kendrick (9-11) for four runs on seven hits in five innings
Philadelphia had entered the contest three games out of a National League wild card spot.