Derby County 1-3 Chelsea

Filipe Luis joined Chelsea from Atletico Madrid in the summer

• Chelsea see off Championship opponents

• Luis scores first Chelsea goal

• Zouma and Drogba pick up injuries

• Derby centre-back Buxton sent off

Filipe Luis struck his first Chelsea goal with a brilliant free-kick to help secure a League Cup semi-final place with a win at 10-man Derby.

Eden Hazard put the Premier League leaders in front and Luis made it 2-0.

Craig Bryson gave Derby hope, but Jake Buxton was harshly sent off before Andre Schurrle wrapped up victory.

Chelsea centre-back Kurt Zouma suffered a head injury and striker Didier Drogba hobbled off, but neither was a serious problem, boss Jose Mourinho said.

Derby centre-back Buxton had a night to forget, having given the ball away before Hazard exchanged passes with Cesc Fabregas and drilled a perfectly-placed shot into the corner of the net for Chelsea's 23rd-minute opener.

But the defender was unlucky to be sent off seven minutes after Bryson had pulled them back into the match.

Referee Jon Moss ruled that Buxton had committed a professional foul by dragging back Loic Remy, although there was no clear appeal from the striker - to the extent that it looked at first as if keeper Lee Grant had been penalised for handling the ball as he slid outside of his penalty area.

The red card destroyed Derby's momentum just as they were threatening to drag themselves back into the match.

And any hopes of a revival were ended when Schurrle slammed in the rebound from eight yards after Grant had parried Remy's shot.

Derby worked hard in the opening 20 minutes to hold off a strong Chelsea side, with Fabregas recalled after suspension in a line-up showing five changes to the one that beat Hull 2-0 in the Premier League on Saturday.

Hazard's opener rocked Steve McClaren's Championship promotion hopefuls, though, and the visitors could have gone further in front as Luis fired an effort straight at Grant and Richard Keogh blocked a Drogba shot.

The match was held up for several minutes at the end of the first half as Zouma was knocked to the ground in a collision with his goalkeeper Petr Cech as Chelsea defended a corner. The French defender needed lengthy treatment on the pitch before he was carried off.

Derby showed fight after the break, with Will Hughes only denied by a combination of Cech and John Mikel Obi after Johnny Russell had set him up.

Their task was made harder as Chelsea doubled their lead when Brazilian left-back Luis - signed from Atletico Madrid in the summer - bent a beautiful 25-yard free-kick beyond Grant.

Drogba then limped off clutching his ankle and Derby pulled one back as Bryson drove Russell's square pass in off the post from 20 yards.

Buxton's red card was a set-back for McClaren's side and Schurrle ended their hopes of an upset.

Derby manager Steve McClaren on Jake Buxton's red card: "I really thought it was going to be a grandstand finish, and we've been robbed. It's a coming together - Remy fouling Buxton, and Buxton coming across Remy.

"Remy's appealing for Lee Grant's handball. We can't believe it's against Bucko. The linesman gave it, not the referee. How he saw that, I don't know. I think he got it wrong. We'll think about an appeal."

Eden Hazard's drive gave Chelsea a 23rd-minute lead - his ninth goal of the season

Eight minutes of stoppage time were added at the end of the first half following Kurt Zouma's injury

Cesar Azpilicueta and Cesc Fabregas help carry the stretcher to the injured Kurt Zouma

Jake Buxton was sent off for a professional foul on Loic Remy - angering Derby manager Steve McClaren

Andre Schurrle wrapped up victory for Chelsea by scoring with eight minutes to go