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Maidstone United will host League 2 strugglers Yeovil Town in the first round of the FA Cup.
Gillingham were the highest ranked team in the draw and they were drawn away to another League 2 team, Stevenage.
Dover were handed a home draw against Stourbridge.
If Welling can see their way past Grays in a replay on Tuesday night they will face either Barwell or Rushden & Diamonds away in the first round proper.
The Gills were knocked out in the first round last season by Bristol City, losing 2-1 at Priestfield.
Maidstone have beaten South Park, Dunstable Town and Chippenham Town to reach the first round proper. Their opponents Yeovil are currently second from bottom in League 2.
Last season the Stones beat Stevenage – Gills’ opponents - at the first round stage before losing to Wrexham in round two.
Maidstone beat Yeovil in the first round of the FA Cup back in 1989 before losing to Exeter in round two.
Dover beat Eastbourne Borough on Saturday to qualify for the first round. They face Evo-Stick Premier Division side Stourbridge, who are sitting just outside the play-offs in their division.
Last season Dover reached round three, losing 4-0 at Crabble to Crystal Palace.
Welling must overcome a Grays team managed by former Gills midfielder Mark Bentley before they can look forward to the first round.
The two teams drew 1-1 on Sunday and the replay takes place on Tuesday night at Park View Road.
Ties will be played on the weekend November 7-8, with dates confirmed once television picks have taken place.
£18,000 is on offer to winners of first round matches.