Eden Hazard sent the Blues into,the semi-final of the a Capital One Cup with a smart first-half strike from just inside the Derby a county penalty area.
Further strikes in the second half from Filipe Luis and Andre Schurrle saw off a brief resistance from The Rams when at 2-0 Craig Bryson notched the home side's only goal with a low drive just outside the penalty area.
The Blues ran out comfortable 3-1 winners at the iPro Arena tonight.
While Chelsea were in total command in the first half, the second was a different story. Derby took the game to the Blues while a degree of complacency crept into the Londoners game.
The visitors took full advantage of the dismissal of Jake Buxton for pulling back substitute Loic Remy to restore their dominance of possession and thus the match. It was after this that Schurrle slotted home his goal.
Who the Blues face will be revealed tomorrow night after the remaining two quarterfinal matches are played tomorrow night.
Cesc Fabregas, said: "These games are always difficult. We knew they would be up for it, but we put out a top side to play them.
"I am enjoying it, the whole squad is playing well.
"We can always do better and we know that and we are trying to do that in training. We are focused. The next few weeks are very important. We are up for it.
"It's all up to us, we have the talent, discipline and courage.
"We will have to work hard to get antsy hang this season."