Cup holders Telford survived early pressure, mainly due to in-form goalkeeper Mitchell Willdigg, but settled down when skipper Dan Frances hit an unstoppable drive into the top corner from 25 yards on the half hour mark.
Benji Robinson doubled the advantage just before the interval, breaking from his own half, leaving 3 defenders in his tracks before slotting the ball past the advancing keeper to offer a cushion for the hosts.
Robinson eventually put the game beyond the visitors 13 minutes from time, cutting in from the right to fire high into the net from the edge of the area to send the youngsters into the semi-final.
Meanwhile, AFC Bridgnorth U18s' 5-1 demolition of Nova United U18s saw them book their place in the semi-final of the cup.
The final two teams will be decided in the first week of February, where Shrewsbury Up & Comers U17s take on Nova United U17s, and Haughmond U18s face Allscott AFC U18s.