Danny Hattersley scored from the penalty spot minutes later to send his side through, where they will face Eastleigh at the Merseyrail Community Stadium.
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Ryan Flynn struck in the 19th minute to fire his side ahead and notched his second of the game 13 minutes from time to guide the Blades through.
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Curtis Main fired the visitors ahead in the 16th minute and Theo Robinson soon scored their second to put them in command of the game.
James Coppinger netted the third on the stroke of half time, and after the break Richie Wellens secured the match with Doncaster's fourth of the evening, while Liam Monelle scored a consolation for the home side.
Ivan Toney fired the visitors in front in the fourth minute, and they held the lead until five minutes from time when Reuben Noble-Lazarus found an equaliser for Rochdale. In stoppage time, Olly Lancashire found the net to allow his side to advance.
The visitors had taken the lead in the 12th minute through Ronan Murray, but the home side responded to book their place in the second round to face Yeovil Town.
Andy Parry and Tony Gray had fired the home side into a 2-0 lead at the break, but Louie Soares fired the visitors back into the game, while Michael Grogan saw red for Telford. However, they held out for the victory and will now face Bristol City.
Mansfield Town and Concord Rangers played out a 1-1 draw as Danny Glozier's own goal was cancelled out by a strike from Jordan Chiedozie. The replay will take place on November 25, while a clash against Cambridge United awaits the winners.
Results in full: Mansfield Town 1-1 Concord Rangers, AFC Wimbledon 3-1 York City, Accrington Stanley 2-1 Notts County, Southport 2-0 Dagenham and Redbridge, Rochdale 2-1 Northampton Town, Weston-super-Mare 1-4 Doncaster Rovers, Shrewsbury Town 1-0 Walsall, AFC Telford United 2-1 Basingstoke Town, Sheffield United 2-0 Crewe Alexandra