Milone (11-9) went five innings, allowing six hits and striking out five in an emergency start, after scheduled starter Jarrod Parker was scratched due to an illness.
Josh Reddick, Chris Young and Josh Donaldson each homered for the American League West-leading Athletics, who completed a three-game sweep of the second-place Rangers.
With their fifth straight win and eighth victory in nine games, the A's increased their lead over Texas to 6 1/2 games, all but assuring themselves of an AL West title.
Martin Perez (9-5) allowed three runs on seven hits over 6 1/3 innings for Texas, which wrapped up an 0-6 homestand with its ninth loss in 10 games.
The Rangers and Tampa Bay, tied with identical 81-67 records, hold the two American League wild-card berths by one game over Cleveland.