A tight encounter was separated by a single goal from Under 15s player Casey Tag shortly after coming off the bench.
The victory over Chesterfield for City's apprentices was all the more impressive given the fact that four of their regular players - Elliott Barker, Sam Wright, Dylan Mottley-Henry and Reece Webb-Foster - were away with the first team at Gillingham.
The Chesterfield win means the Bantams now cannot be caught at the top of the Football League Youth Alliance North East Division with one game to play.
The title success is, of course, City's second in consecutive years after winning the same league trophy last season.