Young doubled with one out against Hector Santiago (1-4), prompting the White Sox to issue an intentional walk to Yoenis Cespedes.
Josh Donaldson, however, drew an unintentional base-on-balls to load the bases, and after Brandon Moss lined out, Reddick coaxed another free pass from Santiago, providing the game-winning run as the A's racked up their eighth win in nine games.
Young finished 3-for-6 with an RBI. Jed Lowrie went 4-for-5 with a run scored in the A's victory.
Jerry Blevens (4-0) got the final out in the top of the 10th to earn the decision after A's starter Dan Straily limited the Chisox one run and struck out eight over six innings.
Alejandro De Aza provided a score-tying, two-run single for Chicago in the seventh inning.