The Blades will travel in the third round of the FA Cup with Budweiser.
Danny Wilson's side will face either Accrington Stanley or Oxford United - both of League Two - in the third round.
Accrington, who include James Beattie in their ranks, drew 3-3 on Saturday with Oxford, who are managed by Chris Wilder, meaning a replay is required.
Two late goals from Shaun Miller secured United's 2-1 success over Port Vale in Saturday's second round tie.
Ties will be played over the weekend of 5th and 6th January 2013, and Untied's League One trip to Bury is postponed as a result.