Newport County 0 York City 0: Run halted by unlikely source
The Minstermen now have a second chance to progress to the last 16 with the winners of the replay due to entertain Corby Town at home on January 30.
Blue Square South leaders Newport dominated the first half with Minstermen keeper Michael Ingham forced into saves from Danny Rose, Sam Foley and Craig Reid.
York improved in the second half with Michael Rankine forcing a goal-line clearance from Paul Cochlin.
Andy Ferrell also tested home goalkeeper Glyn Thompson with a curling free-kick.