Sudden-death penalties proved to be United's nemesis for a second consecutive competitive fixture.
The Capital One League Cup tie finished level with Nick Blackman and Neill Collins scoring for the Blades before the shoot-out drama.
Stephen Quinn, Collins, Kevin McDonald and Tony McMahon netted with spot-kicks but misses by Harry Maguire and Michael Doyle proved costly, with the Blades being eliminated at the first hurdle.
Danny Wilson's first competitive team selection of the season included three debutants in Howard, Miller and McMahon, whilst Westlake and Blackman, who signed 24 hours earlier, were part of a five-man substitutes bench.
The new boys received a warm welcome as the teams were announced before kick-off and once the whistle had gone it was quite clear that McMahon was slotting in at right back and Miller was partnering Porter in attack.
Flynn was prominent early on with a number of corners and free-kicks, whilst goalkeeper Howard's only involvement in the opening 15 minutes was to collect a tame lob from Weir.
Both of United's strikers then went close. On 19 minutes, Porter saw his shot blocked and Miller's long-range effort was parried away for a corner, which was headed just over by Maguire.
Just after the half hour a Flynn free-kick was met powerfully by Porter but Atkins made a reflex save and less than a minute later the visitors opened the scoring. From Kee's pass, YUSSUF picked up the ball on the edge of the box and fired past Howard.
The Blades went close to levelling before the break when Flynn seized on a stray pass from Bell. The winger beat his marker and delivered a cross from the right but Miller's header came back off the far post before Burton scrambled clear.
Blackman was introduced at the start of the second period, replacing Porter, and the replacement took just six minutes to make an impact. A deflected left-wing cross from Flynn looped up for BLACKMAN to head towards goal and Burton's number one, Atkins, made a mess of trying to keep the ball out from under his crossbar.
Another new signing, McMahon, attempted to open his account soon after when shot first time from Flynn's lay-off but Atkins parried away, whilst another debutant was introduced with 20 minutes to go, homegrown teenager McFadzean replacing Miller. The change saw the youngster slot in on the left side of midfield with Quinn taking an advanced central role.
Quinn and Flynn combined on the right on 75 minutes with the latter's cross causing a goalmouth scramble, which Blackman could not convert, but United's attacking intent continued. As the the referee's watch ticked around to 90 minutes, another Blackman shot was pushed out by Atkins and from the loose ball Flynn's low cross to McFadzean was cut out before extra-time was signalled.
The first period of extra-time was then exciting. It began with Blackman rounding Atkins with a deft header but he was unable to net from an acute angle and then Collins had a long range effort pushed away by the visiting goalkeeper before a break, on 97 minutes, saw Burton grab the lead again. From Weir's pass, TAYLOR got the better of Williams before slotting the ball across Howard, into the corner of the net.
Richards and Collins were both booked for fouls on each other within minutes and the drama continued when Stanton was adjudged to have fouled McFadzean in the penalty area after the youngster had linked up with Quinn. COLLINS took responsibility for the spot-kick and although his initial effort was blocked by Atkins, the Scottish defender coolly converted the rebound.
Stanton and Diamond were booked for their protestations before the penalty and the arguments continued afterwards with Holness firstly booked and then sent off for continuing to vent his frustrations.
At the start of the second period Howard was called upon twice to save from Richards, whilst on two occasions the Blades were denied further penalties - McCrory appeared to handle Quinn's shot when he blocked and Diamond looked to have pulled back Blackman.
The second period failed to live up to the first period and penalties - for a second consecutive competitive fixture - was needed to find a victor.
PENALTIES (Blades first)
Quinn - SCORED - powered down the middle
Weir - SCORED - sent goalkeeper wrong way
Collins - SCORED - powerful shot, under the goalkeeper
Bell - MISSED - wide of Howard's right post
Maguire - MISSED - fired over the crossbar
McCrory - SCORED - hammered into corner of net
McDonald - SCORED - coolly placed high in the corner
Webster - SCORED - sent goalkeeper wrong way
McMahon - SCORED - top corner, to goalkeeper's right
Richards - SCORED - low, placed into bottom corner
Doyle - MISSED - saved by goalkeeper, diving to right
Taylor - SCORED - high beyond Howard.
Burton win 5-4 on penalties
Blades: Howard, Maguire, Flynn (McAllister 90), Doyle, Porter (Blackman 45), McDonald, Miller (McFadzean 70), Collins, Quinn, McMahon, Williams.
Unused: Westlake, Long.
Burton: Atkins, Stanton, Diamond, Taylor, Weir, C. Palmer (Dyer 68), Yussuf (Webster 79), McCrory, Holness, Bell, Kee (Richards 60).
Unused: Corbett, M. Palmer, Lyness, Garnett.