Barrow bounced back from their 6-1 home thrashing by Rushden at Holker Street to deny York a fourth straight win.
The Bluebirds produced a battling display to earn a deserved point, but almost went a goal behind early on, Tim Deasy saving Neil Barrett's shot.
The visitors kept pressing and, nine minutes later, Michael Gash's header was goalbound until Deasy tipped the striker's effort over the bar.
Barrow could have won it but Jason Walker's header hit the bar.
Barrow: Deasy, Pearson, Dugdale, Bolland, Jelleyman, Rutherford, Bond, Boyd, Logan, Walker, Taylor (Hulbert 88). Subs Not Used: Tomlinson, Jones, Sheridan, Bayliss.
Booked: Jelleyman.
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York: Ingham, Purkiss, Parslow, Sangare, Meredith, Smith, Lawless, Barrett, Ferrell (Rankine 65), Gash, Brodie. Subs Not Used: O'Hare, McGurk, Nelthorpe, Mackin.
Attendance: 1,120
Referee: Colin Harwood (Manchester).
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