The hosts could not have wished for a better start with an early Liam Holt effort testing Dave Parton and then the opening goal came within 10 minutes. Rhys Thompson exchanged passes with Mitchell Piggon and Thompson let fly a low shot which fizzed in at Partons left hand post.
The Scholars were a dominant force in the firsts half and a second goal just after the half hour was the least they deserved as Holt powered home a header for his second goal in a week.
If Chasetown had been four-up by half time it would have been deserved as Piggon went close with a flick and a strong penalty appeal was turned down for a foul on James Dance.
Newcastle, unsurprisingly, responded at the start of the second half but only forced one serious save out of Curtis Pond on his return from a bruised rib injury.
The visitors had more of the ball in threatening areas but a defence dominated by Jermaine Johnson and Leon Miles kept Castle at bay and clinched a semi-final place.