One out later, Yoenis Cespedes and Chris Carter each singled to put runners at the corners. Brett Myers relieved, and Inge greeted him by smacking a pitch down the right field line, plating Cespedes with the decisive run.
Gomes added a run-scoring single in the ninth while Carter and Derek Norris also finished with two RBI each as the A's evened their three-game series.
Ryan Cook (5-2) earned the win with 1 1/3 scoreless frames and Grant Balfour collected his eighth save for Oakland.
Tyler Flowers went 3-for-3 with a homer and three RBI and Kevin Youkilis added a two-run shot for the White Sox, who maintained a one-game lead over Detroit atop the American League Central.