The Honets will travel to Sandygate Road, just outside of Sheffield, which has been home of Hallam FC since 1860.
Meanwhile, South Shields will host North Ferriby United in the first qualifying round of the FA Trophy. The tie will be played on Saturday, October 27.
North Ferriby sit bottom of the Evo-Stik Premier League table, but handed out a shock 3-0 defeat to Shields earlier this season.
The 16 places where most crime was reported across South Tyneside in June
‘Bully’ broke disabled girlfriend’s arm and dragged her through broken glass in shocking campaign of cruelty
‘Sinister’ paedophile watched children play and offered them doughnuts after moving into new neighbourhood
Extension plans rejected for South Shields home
13 great pictures as the sunshine sees crowds flock to South Shields beaches
Hebburn beat City of Liverpool 4-0 on Saturday in the first round of the Vase a game which featured a stunning 45-yard strike from James Fairley.
The Hornets are one of the favourites for the competition, with a squad packed full of former winners, including ex-South Shields men Andrew Stephenson, Michael Richardson and Louis Storey.
Hallam, who sit sixth in the Northern Counties East league Division One table, have won six of their last seven games and beat Charnock Richard 3-1 on Saturday in the Vase.
Other Vase ties involving Northern league sides are:
Vauxhall Motors v Runcorn Town or Guisborough TownStaveley MW or Silsden v Bedlington TerriersNewcastle Benfield v 1874 NorthwichWinterton Rangers v Dunston UTSBarton Town v ShildonGarstang v Sunderland RCAThackley v West Auckland TownStockton Town v Nelson or Ashington