The A's erased a 3-1 deficit in the seventh on a two-run double by Josh Reddick, and then went on to win it in the ninth when Hicks -- who had come into the game as a pinch-runner -- blasted a pitch from Michael Kirkman (0-1) into the right-center field seats.
The game-ending homer gave the A's their ninth walk-off win of season, the most in the majors, and allowed them to split the two-game series.
The clout made a winner of Ryan Cook (3-2), who blanked the Rangers in the top of the ninth despite allowing a single and a walk.
Brandon Inge went 2-for-4 with a solo homer for the A's, who improved to 10-2 in July.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys