French striker Wesley Ngo Baheng could have put the Toon ahead against the Bantams but shot straight at home goalkeeper Jon McLaughlin.
Within five minutes City were in front, Leon Osborne latching onto an incisive through ball before firing beyond Ole Soderberg.
McLaughlin saved from Frank Danquah to keep the home side in the lead, and saved again from Shane Ferguson who tried his luck with a 20-yard free-kick.
City doubled their advantage on 54 minutes.
Osborne was again the scorer, this time scoring off the post.
NEWCASTLE UTD RESERVES: Soderberg, Morris (McGorrigan 52), Ferguson, McLaughlin, Tozer, J. Taylor, Godsmark, Donaldson, Ranger, Baheng (Edmundsson 86), Danquah (Spear 54). Subs n/u: McCrudden, Johnson