The Blades booked a place in the third round of the cup and could face a Premier League team in the next round; but had the tough job of overcoming MK Dons first.
United eventually won this tie after going a goal behind but had to take it into extra-time were Geoff Horsfield popped up with the winner.
The veteran striker capitalised on a spill by former Luton Town keeper Nathan Abbey in the 103rd minute to send the Blades into the next round.
It was however the home side who went in front via Drewe Broughton who slid in to flick home Jude Sterling's low cross on the 11th minute.
And, nine minutes later the scores were even when United won a corner on the right hand side for Nicky Law to produce a clinical cross only to be met by the head of defender Chris Lucketti to net his first ever Blades goal.
The home side dominated the remainder of the first half with Alan Navarro curling his 22 yard shot wide.
The Blades upped the tempo in the second half and went ahead when David Carney's shot was saved by Abbey but dropped to Nicky law who dispatched (55) his first professional goal.
With twelve minutes left the Dons were level when Jon-Paul McGovern saw his free-kick deflected wickedly off the wall and into the goal.
But Horsfield slotted in the winner from close range 13 minutes into the first period of extra-time after Luton Shelton's fizzing 22-yard drive had been spilled by Abbey.