The Athletics were trailing 2-0 in the seventh inning when Coco Crisp led off with a single and Donaldson followed one out later with a score-tying blast off the facing of the second deck in center field.
After pinch-hitter Derek Norris drew a base on balls, Donaldson blooped a hit to right field, sending Young home with the game-winner.
Ryan Cook (2-2) pitched two scoreless innings to earn the win as the American League West-leading A's went into the All-Star Game break by taking the rubber match of a three-game set against the AL East leaders.
Dustin Pedroia and Brock Holt each drove in a run for the Red Sox, who went into the break with a 2 1/2-game advantage over Tampa Bay.
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