High-flying United killed off Second Division Cheltenham's cup dream with goals from Shaun Murphy and Jon-Paul McGovern in a nine minute first-half spell.
But it was lazy performance from the Bramall Lane side and manager Neil Warnock will be looking for more effort from his side for the mouth watering Worthington Cup semi-final clash against Liverpool on Wednesday.
Mark Yates tested United keeper Paddy Kenny with a long range strike and John Finnigan had a right-foot strike blocked as Cheltenham looked for an early opening.
But is was United who swept ahead in the ninth minute Murphy stabbing in McGovern's corner after the Cheltenham defence failed to clear the Australian centre back's close-range header seconds earlier.
Canadian international Paul Peschisolido picked out midfielder Nick Montgomery minutes later but he squandered the chance firing straight at Steve Book from 16 yards before United added a second in the 20th minute.
Steve Kabba had time on the let flank to pump over a low cross, Peschisolido cleverly stepped over the ball as McGovern steamed in to crack it past the helpless Book from 12 yards out.
Michael Tonge was foiled at the near post by the Cheltenham keeper on 32 minutes, Book spreading his body to block the young midfielder's fierce strike after McGovern's cross had flicked off the head of Michael Duff.
Phil Jagielka almost snatched a third after 60 minutes with a stinging shot from the edge of the area spectacularly pushed round the post by the acrobatic Book before Kabba added a third in the 63rd minute, exchanging passes with Peschisolido before steering the ball into the left hand corner of the net.
Kabba added the fourth with a close-range header six minutes from time.
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