A thoroughly professional performance secured United's passage into the fourth round of the FA Cup.
For the second successive season, the Blades proved to be Oxford's nemesis in the competition.
Another Tony McMahon free-kick set the ball rolling, whilst second half goals from Dave Kitson and Nick Blackman ensured the Blades inflicted Chris Wilder's Oxford's first defeat in 11 games.
For the first visit to the Kassam Stadium, Murphy, wearing number 23, was handed his debut and Maguire returned to the starting line-up after suspension - Kennedy and Whitehouse dropped to the bench.
Kick-off confirmed that Murphy was partnering Kitson in a central role, with Blackman and Flynn continuing on the flanks. United's first chance came from an unlikely source, Hill forward to flick on a Doyle cross but the subsequent accidental collision with Wright was a painful one and the Blades defender was substituted soon after, Williams was the replacement at left-back.
Oxford's Heslop twice fired over and Craddock followed suit, only finding the car park at the three-sided ground, whilst for the Blades Kitson and Blackman both went for a floated Flynn cross and put each other off - ahead of the Blades taking the lead. Blackman fed Murphy to run at the home defence and he was upended on the edge of the box by Wright, allowing McMAHON to step up and continue his good run, curling over the defence and leaving goalkeeper Clarke rooted to his starting position.
Oxford attempted to hit back but Craddock's shot was pushed away by Long after the Blades had backed away from a throw and then Higginbotham produced a good header to prevent Potter connecting with Capaldi's cross.
Backed by their partizan crowd, appealing for every decision, Oxford continued to look for an equaliser and Craddock had the ball in the net but he was adjudged to have fouled Long, whilst five minutes of added time - mainly due to Hill's early injury - failed to earn the home side a leveller.
The Blades made a positive start to the second half, winning two corners and going close twice following Blackman's run down the right but shots from Doyle and Murphy were blocked. Oxford then wasted a great chance on 54 minutes when Craddock's head down was perfect for Richards but the striker, despite being in space, clipped wide as Long came off his line.
Potter also shot at Long but the Blades came close to adding to the lead, firstly when Murphy was pulled down by Duberry but referee Boyeson indicated no penalty and then a half-volley from McDonald was not far away from hitting the target.
Doyle picked up the game's first yellow card for foul on Leven, moments before the Blades made the second half pressure pay by doubling the advantage. With 68 minutes gone, Flynn's inswinging free-kick was headed back across goal by Blackman and KITSON made sure the ball crossed the line by touching in from close range.
Murphy set up Blackman soon after but the leading scorer's shot was deflected just wide and Ironside replaced Kitson with just under 15 minutes remaining.
Rigg shot across goal and wide and then forced a save out of Long with nine minutes remaining. Craddock pushed Williams but couldn't use the good fortune of not giving away a free-kick to find the target and the Blades added a third late on to put the seal on the victory. McDonald clipped forward and BLACKMAN held off his marker, took a neat touch and fired into the roof of the net on 87 minutes.
Job done, Murphy was replaced by Cresswell and the Blades defence, as they had done all afternoon, remained solid for the remainder of the game to chalk up a deserved clean sheet.
Oxford: Clarke, Batt, Duberry, Wright, Heslop, Potter, Capaldi, Richards, Leven, O'Brien (Rigg 67), Craddock.
Unused: Raynes, Brown, Worley, Parker, Marsh, O'Dowda.
Blades: Long, Higginbotham, Maguire, Hill (Williams 12), Flynn, Doyle, Blackman, McDonald, Kitson (Ironside 76), Murphy (Cresswell 89), McMahon.
Unused: Tonne, Whitehouse, Kennedy, Coyne.