United booked a place in fourth round of the League Cup for the first time in seven years - thanks to Michael Higdon's early goal.
The big striker netted just two minutes in to the Capital One Cup third round tie at Leyton Orient.
The victory continued Nigel Clough's impressive cup record with the Blades extending to just one defeat (at Wembley) in 11 matches.
Goalkeeper Howard was named as captain as boss Clough made six changes. For the all-League One tie, Harris, Wallace, Reed, McGinn, Flynn and Higdon all returned, meaning Doyle, Davies, Scougall, McEveley and McNulty dropped to the bench, Basham missed out. Ex Blade Henderson was among Orient's substitutes.
Murphy won a corner within the first 30 seconds and although that was cleared, the winger was not long in making another telling contribution. Less than two minutes had elapsed when Murphy beat Cuthbert and supplied the cross for HIGDON to climb above his marker and head past Woods, in front of the travelling Blades.
Two minutes later Murphy could have doubled the advantage when he connected with Flynn's pull-back from the right flank but the subsequent shot flew over the crossbar.
After getting over the initial onslaught, Orient hit back. McAnuff fired at Howard from the edge of the box and Simpson's delivery flew across the six-yard area, whilst Alcock and Harris were kept busy.
In an entertaining opening half hour, the next Blades chance also fell to Murphy, operating from the left. He collected Alcock's diagonal pass, cut inside Pritchard and waited patiently to get a shot away but Woods saved.
Late on in the half, as United purposefully repelled the home side, the only further chance was a 35-yard effort from Mooney, which Howard dropped to save after quickly adjusting his feet.
The first opportunity of the second period dropped for the home side but McAnuff's effort was across goal and wide. Wallace's battling qualities came to the fore on 54 minutes when he won possession back twice before forcing a save out of Woods.
With time running out, Orient were looking to force United back but the visitors were disciplined. Simpson's back header was comfortable for Howard and Omozusi's shot deflected off Flynn and clipped the outside of a post.
On the break, Murphy and Reed linked up but McGinn's shot was wide and Orient's intentions were clear when Henderson was brought on for the last 20 minutes - Alcock did well to clear a teasing cross soon afterwards. Doyle was also introduced, for the tiring Wallace, and was booked for a clash with Vincelot.
Porter replaced Higdon with less than 15 minutes to go but Orient remained the more offensive side. Omozusi again tried his luck from range but Howard watched the effort all the way and collected, whilst McAnuff fired over.
The final ten minutes passed with very few incidents - testament to United's professional display - although Porter connected with Alcock's cross and forced Woods to collect. Flynn was booked for wasting time and in the final of four minutes of added time Vincelot headed over the home side's final chance as the Blades moved into the fourth round.
Orient: Woods, Omozusi, Vincelot, Cuthbert (Pritchard 11), Baudry, James, Mooney (Henderson 69), McAnuff, Clarke, Petrasso (Cox 62), Simpson.
Unused: Batt, Bartley, Dagnall, Grainger.
Blades: Howard, Alcock, Harris, Wallace (Doyle 67), Flynn, Murphy, McGinn, Collins, McGahey, Higdon (Porter 77), Reed.
Unused: Scougall, McNulty, Davies, McEveley, Turner.