The Bantams' under 18's overcame a two-goal deficit to defeat the Millers 4-2 in their second round encounter.
Two goals from youth team top scorer Oliver McBurnie - his twentieth and twenty-first strikes of the season - and efforts from Reece Webb-Foster and Nathan Curtis ensured City's place in round three.
The cup victory means City's apprentices are now unbeaten in their first fifteen games of the season in all competitions. The youth team have only dropped two points in the league so far - a run which has understandably led them to the top of the North East Youth Alliance table. They are also through to the F.A Youth Cup third round.
City's third round tie in the F.A Youth Cup is against Milwall on Tuesday 17 December 2013 at the Coral Windows Stadium.