Nigel Clough's men, who reached the semi-finals last season, sealed progression as a pair of Jose Baxter penalties put them 2-0 to the good after 62 minutes, with Mark McNulty putting the gloss on the victory in the last minute.
Preston North End, two-time winners themselves, secured a 1-0 success against Shrewsbury Town, defender Paul Huntington settling the tie in the Lancashire club's favour with a 19th-minute effort.
Meanwhile, MK Dons tumbled out of the competition as they were beaten 1-0 at home by Chesterfield, and Oldham Athletic lost to Doncaster Rovers by the same scoreline courtesy of Genseric Kusunga's 86th-minute own goal.
Kwesi Appiah scored in the second minute of injury time to earn a replay for Cambridge United as Richard Money's men drew 2-2 with Mansfield Town in Adam Murray's first game as permanent manager.
League Two Accrington Stanley held League One Yeovil Town to a 1-1 draw, while Daniel Nardiello netted in the 91st minute to ensure a 1-1 draw for Bury at home to luton Town.
Elsewhere, Oxford United drew 2-2 with Tranmere Rovers.
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