The Tigers needed a late goal from striker Nick Proschwitz to earn another chance to defeat Leyton Orient after their 1-1 draw in the third round on Saturday.
Steve Bruce's side have already beaten the Tykes this season, when Sone Aluko's strike secured a 1-0 victory back in November.
The tie will be played on the weekend of 26/27 January.
- Sports & Recreation
- Nick Proschwitz
- Leyton Orient
- Steve Bruce