Goals from Eden Hazard, Filipe Luis and Andre Schürrle saw Chelsea run out 1-3 winners over Derby to progress to the Capital One Cup semi-final with the Rams’ consolation goal coming via a great finish from Craig Bryson.
The Rams’ put in a more than spirited performance that their supporters could be proud of, but in the end, the former European champions always had a little too much for the hosts.
A red card with around ten minutes to go for centre back, Jake Buxton, made things even more difficult for Derby and as the referee brought proceedings to a close, Derby slipped out of the cup.
The Premier League side showed their quality as they edged the opening period, but Derby gave a good account of themselves, playing neat football when in possession and defending well.
But one mistake proved costly as a slip from Richard Keogh allowed Hazard in and the Belgian didn’t need a second invitation to slap a low effort past Lee Grant to open the scoring.
Derby came out for the second half full looking determined to turn things around, but they were caught on the break and when Didier Drogba was upended, Luis stepped up to take the free kick and smashed his effort into the top corner.
The Rams hauled themselves back into the tie with fifteen minutes to go, with Bryson curling a superb strike in off the post, but two minutes later, Buxton was dismissed for bringing down Remy as he raced through on goal.
After that, a third Chelsea goal was always on the cards and despite Grant making an excellent save from a Loic Remy shot in the dying minutes, Schürrle smashed in the rebound from close range to seal the victory.
Despite being a league apart, the two sides appeared relatively evenly matched during the opening 20 minutes, albeit without any significant scoring opportunities.
Derby started brightly, knocking the ball around neatly and getting at their opponents often, but they were unable to carve out a clear chances. Meanwhile, Chelsea kept the ball well in midfield, but found it equally different to break down a disciplined Rams defence.
But, the away side would draw first blood in the 21st minute, when a mistake from Rams’ skipper, Richard Keogh, saw the ball fall to Hazard, who rounded Buxton and placed a hard low shot past Grant.
Five minutes later and another chance fell the way of the visitors, as full back, Luis, found himself in space just inside the Rams’ box, but his powerful effort was straight at Grant, who easily palmed it away.
Cesc Fabregas was next to try his luck, as he skipped past Buxton and smacked a left foot effort goalwards, but his aim was off and the ball rolled harmlessly wide of the left upright.
Derby started to gain momentum as the half wore on, testing the Chelsea back line on a number of occasions, but were unable to find a breakthrough.
A nasty collision with his own keeper saw Kurt Zouma stretchered off the pitch and replaced by Branislav Ivanovic in first half stoppage time and the opening period was brought to a close with Chelsea leading.
Derby roared out of the blocks in the opening moments of the second half, throwing everything at the Blues and creating their first big chance of the game.
Johnny Russell used his pace to glide past his marker down the right wing before pulling the ball back to Will Hughes, who forced Petr Cech into an excellent low save with his first time effort.
But it was the visitors who doubled their advantage in the 56th minute when Drogba won a free kick just outside the Derby area and from the set piece, Luis struck a powerful left-foot strike into the top corner.
That goal could have knocked the wind out of the Rams, but instead of letting their heads drop, the home side rallied and set about trying to find a way back into the tie.
And their hard work paid off with 20 minutes to go as Johnny Russell worked his way into the area before laying the ball off to Bryson who curled a shot past Cech and found the back of the net via the inside of the post.
The Rams’ chances of equalising took a blow in the 75th minute when Remy bore down on goal before being adjudged to have been pulled back by Derby’s last man, Buxton.
Referee, Jonathan Moss, consulted his line man before going to his back pocket and showing the defender a straight red card, leaving the home side with a mountain to climb.
With less than ten minutes to go, with Derby searching for a second goal, Chelsea made the most of their numbers advantage.
Remy’s low shot from inside the box was saved well by Grant, but the Derby ‘keeper could only parry the effort as far as Schürrle who pounced to make it 1-3 and all but kill the tie.
Derby County: Grant (GK), Christie, Forsyth, Bryson, Buxton, Keogh (C), Dawkins (Ibe 57), Martin, Russell, Hughes (Hendrick 76), Mascarell (Best 84)
Substitutes not used: Roos, Naylor, Coutts, Calero.
Chelsea: Cech (GK), Luis, Fabregas, Zouma (Ivanovic 45+4), Hazard (Ramires) 83), Drogba (Remy 63), Obi Mikel, Schurrle, Matic, Terry (C), Azpilicueta
Substitutes not used: Schwarzer, Salah, Costa, Willian
Attendance: 30,639 (3,024)