The sparkling early-season form shown by Southampton now seems but a distant memory after a second-half goal from Mark McNulty inflicted a fifth straight defeat on the Premier League club who were reduced to 10 men late on when Florin Gardos was sent off.
It was a much more relaxed evening for league leaders Chelsea who went 2-0 up with a goal from Eden Hazard and a stunning free kick by Filipe Luis before second tier Derby pulled one back through Craig Bryson.
A late charge was curtailed, however, when the home side's Jake Buxton was sent off for a professional foul on Loic Remy and Andre Schuerrle ensured there were no late jitters when he slammed home a Chelsea rebound from close range in the 82nd minute.
The confidence seems to have drained from Southampton whose early surge up the league on the back of some favourable fixtures has turned into a widely predicted slump.
United, managed by former Liverpool forward Nigel Clough, were not going to prove accommodating opponents for the Saints to regain some much-needed confidence.
While boasting the usual battling traits of a lower-league side when facing top-flight opposition, the club known as The Blades also came with an impressive cup pedigree.
United had lost only two of their previous 17 cup clashes and had ousted three Premier League teams from knockout competitions in the last two seasons.
They did their best to unsettle Southampton from the start and shaded the first half chances before finding a breakthrough after halftime.
When Southampton keeper Fraser Forster fumbled a free kick, McNulty was there to force the ball over the line.
STRONG SIDE
Chelsea have suffered some quarter-final blues of their own in recent times but fielded a strong side in an effort to avoid a repeat of last year's surprise last-eight defeat at Sunderland.
The manner of their victory was one of ruthless professionalism, typified by Spain midfielder Cesc Fabregas who continues to catch his manager's eye.
"Cesc is playing so well for us," Jose Mourinho told Sky Sports television. "What I like is as a person he is a professional.
"He is a world champion, he comes here to play in the Capital One Cup and plays like that. That is the character I like."
Four-times winners Chelsea never looked in much danger and went ahead after 23 minutes when Hazard made the most of a defensive mishap.
Derby defender Richard Keogh was robbed of possession on the edge of the penalty area and Fabregas swiftly fed the Belgian who kept his composure before drilling the ball low into the net.
The hosts had plenty of possession but could not lay a glove on Chelsea whose only real worry in the first half came when defender Kurt Zouma had to be stretchered off following lengthy treatment after a clash of heads with keeper Petr Cech.
Will Hughes had a Derby effort pushed away by Cech before Filipe Luis took aim with a free kick from distance and smashed the ball high into the top corner in the 56th minute.
Chelsea did not have it all their own way and conceded with 19 minutes remaining as Bryson curled home from the edge of the box. But Buxton's red card and Schuerrle's late effort guaranteed there was no unexpected drama.
Wednesday's two quarter-finals pit second tier Bournemouth against eight-times winners Liverpool while Tottenham Hotspur host Newcastle United.
(Editing by Tony Jimenez)
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