Cup exit for Millers at York
Ronnie Moore’s men paid for missed chances in the first half as the Minstermen booked a trip to another Blue Square Premier club, Darlington, in the second round.
Chris Smith headed them into a 66th minute lead and Michael Rankine made it 2-0 from the penalty spot on 71 minutes after he was tumbled by Luke Ashworth.
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Rankine then steered in his second of the game on 79 minutes to put the issue beyond doubt.
Rotherham had the better of the first half, with Stephen Brogan hitting the inside of a post and Nicky Law and Adam Le Fondre also going close but York survived to spring an upset.
York City: Ingham, Parslow, Meredith, McGurk, C. Smith, McDermott, Sangare, J. Smith, Carruthers, Racci, Rankine.
Millers: Annerson, Mullins, Newey, Ashworth, Fenton, Marshall, Bradley, Law, Brogan, Le Fondre, R. Taylor.