Joe Oates scored 'Side's winner, from the penalty-spot on 75 minutes.
The result, Alex Goldstone's first win in charge since being appointed Interim Manager, see's the Sky Blues advance to the quarters of the competition.
They will face Saffron Walden Town at home, with the winners of that tie going on to the semi-finals. A date for this match at Cricklefields will be announced in due course.
'Side: Mikel Breckenridge, Edward Buchanan, David Ottley, Harry Matthews (James Coppins), Charlie Peters-Hey, Derek O'Halem, Joe Oates, Darnell Goather-Braithwaite, David Hornsby (Garjay Thompson), Terry Anim (Shaiquan Maisara), Akwasi Marfo