York striker Richard Brodie scored twice against former club Barrow to put City fourth in the table.
Barrow enjoyed the better of the first-half chances as Michael Ingham kept out Andy Bond's effort and Paul Jones and Carlos Logan both missed the target.
And prolific Brodie made them pay when he headed home Chris Carruthers' cross.
Nick Chadwick missed two headers for Barrow before Brodie showed him how it was done again with his head, and Michael Gash drilled home late on.
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