With the score tied 3-3 starting the sixth, Zach Miner (0-1) came in to pitch and Castro greeted him by pounding a pitch deep over the center-field wall.
Cole Gillespie drove in two runs and Welington Castillo added an RBI as Chicago rebounded from a 6-5 loss in Friday's three-game series opener.
Carlos Villenueva (3-8) earned the decision with 1 1/3 shutout relief frames and Kevin Gregg secured the win with his 28th save.
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