The Whites overcame Conference side Grimsby Town 3:2 (AET) at Blundell Park on Tuesday evening to seal a trip to Bramall Lane on the 7th of January.
Salisbury took the lead on 46 minutes, but the Mariners equalised right at the death to send the game into extra time.
Grimsby then took the lead for the first time in the game, but Salisbury replied with two goals of their own to record a 3:2 away victory.
Wins over Oxford and Torquay ensured United's place in the Third Round, with the Fourth Round place seeming a good possibility.