City go into the game with a slight advantage having won the first leg 3-2 at St James' Park last week.
Kelvin Etuhu gave the Blues a deserved lead in the 26th minute when he scored from an Ashley Williams pass. It was Etuhu's fifth Youth Cup goal in five games, while he has scored 16 in 18 Academy games this season.
Newcastle got themselves level just before the break through Jonathan Godsmark, and Godsmark struck again just after the restart to give the Magpies an undeserved lead.
But City soon struck back through Williams, whose six-yard volley levelled things up after 50 minutes.
The Blues then got themselves back in front when Williams played Michael Johnson through on goal in the 57th minute and the captain made no mistake.
That gave City a vital lead going into the second leg although they could have made it more comfortable late on.