A late Rangers comeback, courtesy of Akos Buzsaky's penalty and Damion Stewart's header, set up a nervy finish but the hosts were unable to arrest their dismal FA Cup record.
They have not won a single tie in the competition since 2001 - a run now stretching 13 games - so it was little surprise to see United join a list of teams including Luton, Grimsby and Vauxhall Motors in sending them spinning out at the first hurdle.
Chairman Flavio Briatore was back watching his team for the first time since his motor racing ban was lifted.
But they have now managed just one win in their last 10 games and were often booed by those who had bothered to turn up.
The empty seats all around the ground illustrated just how little this third-round replay had captured the imagination.
And for United, the prospect of a trip to Bolton in round four is unlikely to set the pulses racing.
Rangers went close through Mikele Leigertwood and Alejandro Faurlin in the first five minutes, but the Blades went ahead against the run of play.
Williamson gathered Nick Montgomery's curling cross on the angle of the Rangers penalty area and drilled a low shot across Radek Cerny.
Ched Evans should have doubled the lead when he raced through with only Cerny to beat, but the former Manchester City youngster's lob came back off the crossbar.
Moments later the visitors were indebted to Derek Geary for preserving their advantage, the defender clearing Kaspars Gorkss' header off the goal-line.
But the arrival of Ward, who started on the bench amid reports of a contract dispute at Bramall Lane, sparked the game into life.
The striker netted with his first touch when he met Stephen Quinn's cross in the 68th minute.
And seconds later Ward charged down the right wing and centred for Cresswell to tuck the third past a shell-shocked Cerney.
Rangers were gifted a lifeline when Geary was adjudged to have handled and Buzsaky converted the penalty.
And hopes of a dramatic fightback were raised when Stewart headed in Buzsaky's free-kick with two minutes remaining.
But a point-blank save by Blades keeper Mark Bunn from Antonio German in stoppage time secured his side the dubious honour of a trip to Owen Coyle's Bolton later this month.