AFC Wimbledon's reward for their FA Trophy win at Aldershot is an away match against Gravesend and Northfleet. The second round draw also pitted Histon, who stunned local rivals Cambridge United 5-0, against Conference South rivals Newport County.
Holders Grays Athletic have been handed a trip to Weston-super-Mare, while Yeading and Bishop's Stortford, who both enjoyed first-round upsets, meet.
The last-32 ties are scheduled to be played on Saturday 13 January.
FA Trophy Second Round draw:
Stalybridge Celtic v Kettering Town
Oxford v Halifax
Morecambe v Mangotsfield United
Altrincham or Tamworth v Welling United
Newport County v Histon
Eastbourne Borough v Northwich Victoria
Exeter City v Kidderminster Harriers
Salisbury City v Southport
Redditch United v Dagenham & Redbridge
Worcester City v Burton Albion
Witton Albion v Rushden & Diamonds
Weston-Super-Mare v Grays Athletic
Farnborough Town v Braintree Town
Stevenage Borough v Leigh RMI
Yeading v Bishop's Stortford
Gravesend & Northfleet v AFC Wimbledon
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