Facing a full-count pitch from Daniel Webb (5-4) with the bases loaded, Prado lined a hit up the middle to complete the Yankees' comeback from three runs for their fourth win in 11 games.
Prado hit a two-run homer in the third, and Jacoby Ellsbury had an RBI double in the fifth off John Danks after Chicago's Jose Abreu connected for a three-run shot in the first against Shane Greene.
Ichiro Suzuki started the ninth with a single and advanced on a sacrifice. After Derek Jeter lined out, Webb intentionally walked Ellsbury and walked Mark Teixeira before Prado's hit touched off a celebration near second base.
David Robertson (2-4) struck out two in a perfect ninth. Chicago (59-69) fell a season-high 10 games under .500.
