Weymouth play in the Southern Premier League and progressed in bizarre circumstances - when opponents Needham Market withdrew from the competition.
Their first round tie was postponed due to the weather at the weekend, and Needham decided to withdraw saying it was "completely unreasonable" to attempt to play the game again this Tuesday.
After a goalless draw at Borough Park on Saturday, the two EVO-STIK League sides will go again to make it through to the last 32.
With Farsley Celtic, Lancaster City and Basford United all going down to higher league opponents on Saturday, there will be just one NPL representative in the second round.
The second round tie will take place on Saturday January 12.
Draw in full:
Workington/Ramsbottom v Weymouth
Hartlepool Unitedv AFC Telford United
Woking/Maidstone United v Maidenhead United/Oxford City
Hemel Hempstead v Wingate and Finchley
Barnet v Dorchester Town
Hereford v Brackley Town
Salford City/Gateshead v Dagenham and Redbridge
Blyth Spartans v Boreham Wood
AFC Fylde v Biggleswade Town
Spennymoor Town v Bromley
Stockport County v Truro City
Dover Athletic/Havant and Waterlooville v Harrogate Town
Chesterfield v Aldershot Town/Bedford Town
Carshalton Athletic v Salisbury/Braintree Town
FC Halifax Town v Solihull Moors
Wrexham v Leyton Orient