Hughes had given up just one run through his first six innings, but loaded the bases in the seventh before manager Joe Girardi pulled the starter in favor of Boone Logan.
Logan ended up giving up a run on a wild pitch, then surrendered a double to Denard Span, giving the Twins two more in the frame. A Joe Mauer single scored Span from second base to give the Twins a 5-3 lead before Justin Morneau fouled out to end the inning.
The Yankees had built a 3-1 lead on the strength of home runs from Nick Swisher and Russell Martin earlier in the game. A two-out, ninth-inning homer from pinch hitter Andruw Jones brought the score to 5-4, but the Yankees could not score again.
The Yankees (89-65) remain 1½ games ahead of the Baltimore Orioles in the American League East race with eight games remaining.