Filipe Luis
Luis' free kick helped ease Chelsea into the final four.Getty

Filipe Luis' first Chelsea goal helped guide the Blues into the semi-finals of the League Cup with a 3-1 win over Derby County.

Goals from Eden Hazard and Filipe Luis put Chelsea ahead before the Championship side rallied after pulling a goal back through Craig Bryson.

But a red card shown to Jake Buxton killed off the fight back from Steve McLaren's side.

It was Buxton's error that led to Chelsea's opener after 23 minutes when his loose pass was pounced upon by Hazard, who played a neat one-two with Cesc Fabregas before drilling a fine effort past Lee Grant.

Just over 10 minutes into the second half Chelsea doubled their lead as Luis, a summer signing from La Liga champions Atletico Madrid, curled a precise free kick into the corner of the net from 25 yards out.

Derby's resilience eventually paid off as Bryson pounced on Jonny Russell's pass to score from 20 yards out with 19 minutes remaining on the clock. However, that momentum soon evaporated when Buxton was harshly shown a red when Jon Moss ruled the defender had committed a professional foul for dragging back Loic Remy, despite their being no appeal from the Chelsea striker.

Andre Schurrle killed off Derby's hopes with a third soon after.

Jose Mourinho's side will be joined in the final four by Sheffield United who inflicted more misery on Southampton through a 1-0 victory at Bramall Lane.

It marks the fifth consecutive defeat in all competitions for Ronald Koeman's side who struggled to impose themselves on the League One side who took their lead after an hour after Marc McNulty reacted quickest to tap home after Fraser Forster spilled a free kick.

Saints centre half Florin Gardos was also sent off on his first start on another miserable evening for the south coast club.

Koeman was also left furious with Blades' boss Nigel Clough, accusing the United bench of showing a lack of respect while celebrating their goal and refused to shake his hand after the match.

"I shake hands with people who have respect for me and have respect for the fourth official," the Dutchman said.

"I think the behaviour of Sheffield United's bench, I never saw that."

Championship leaders Bournemouth host Liverpool, while Tottenham Hotspur meet Newcastle United in Wednesday's two semi-finals.