Published: 13:08, 11 November 2019
| Updated: 13:28, 11 November 2019
It means the teams will go head to head on successive weekends with the Darts hosting a league match between the sides at Princes Park this Saturday.
They also have a third meeting to arrange before Christmas with the teams paired together at the Gallagher in the second round of the Kent Senior Cup.
Mark Goldberg's Welling also face a fellow National League South side, with a home game against St Albans - who won at Park View Road in the league last month.
Folkestone play their second qualifying round match at Maldon on Wednesday night, delayed from the weekend due to their hosts' FA Cup tie with Leyton Orient.
The winners will travel to Enfield Town, who sit fourth in the Isthmian Premier, in the next round.
Winning teams will pick up £3,750 with losing sides earning prize money of £1,250.
FA Trophy third qualifying round draw (ties to be played on November 23): Enfield Town v Maldon or Folkestone, Maidstone v Dartford, Tonbridge v Bognor, Welling v St Albans.
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More by this authorMatthew Panting