The Abbotts drew 1-1 with Livingstone RARA at Capershotts on Sunday before knocking their visitors from the Morden and District Sunday Vets League out of the competition on penalties.
Bury Town host the Metropolitan Police in the next first round tie to take place on Wednesday night.
Other teams competing in this year's competition include Aveley, Brentwood Town, Leiston and Waltham Forest.
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