After being mainly reduced to efforts from distance during the first half, Jose Mourinho’s side eventually broke the deadlock just after the hour mark when John Obi Mikel headed home Willian’s free-kick.
The influential Oscar wrapped things up for the visitors just five minutes later when his strike was too powerful for Derby goalkeeper Lee Grant to handle.
It was far from straightforward for the visitors, who will now face Stoke, as the fourth round draw was concluded minutes before kick-off.
Derby entered the game on the back of a 1-0 New Year’s Day defeat by Wigan, their first loss in 10, while Chelsea were full of confidence having won their last three Premier League games.
It was Mourinho’s men who had the first sight of goal, though, as Samuel Eto’o attempted to catch Grant out with an ambitious lob, but his effort could only find the stands from distance.
Backed by a vociferous home crowd at Pride Park, Derby were ensuring that the Blues had difficulty breaking down their hosts as Eto’o was smothered by Grant before Michael Essien fired wide, but clear-cut chances were scarce for either side in the opening stages.
The Rams were doing well to restrict Chelsea to shooting from range and this was reflected again as Ramires struck wide from some way out before Oscar’s free-kick curled inches away from Grant’s post.
The Brazilian then fired over the bar, again from distance, after escaping Jeff Hendrick and at the other end, John Eustace could only find the arms of Mark Schwarzer after dispossessing Ramires.
Oscar saw yet another long-range strike evade the crossbar before Ramires’ deflected effort clipped the post as the tie remained deadlocked at the break.
Chelsea came out from half-time full of intent, with Jake Buxton forced to clear Oscar’s cross from within inches of the goal line almost immediately after the teams had re-emerged.
Derby then threatened through Jamie Ward, curling a free-kick over the bar, after Will Hughes was clipped by Mikel.
In an attempt to open things up, Mourinho sacrificed captain for the day, Michael Essien, for the more attack-minded Eden Hazard and Fernando Torres then replaced the ineffective Eto’o.
However, it was through the unlikely source of Mikel that Chelsea eventually took the lead as the midfielder flicked Willian’s near-post free-kick past a helpless Grant in the Derby goal.
Ramires was then booked for diving when there was no contact from Michael Keane in the Derby box, before Chelsea claimed a second via Oscar on 71 minutes.
The Brazilian had been problematic for Derby all afternoon and after exchanging passes on the edge of the area with Torres, his swerving strike was too powerful for Grant and the goalkeeper could only parry it into the back of the net.
Torres then had two chances in quick succession to make it three, initially being denied by the feet of Grant after the Spaniard looked to round him, before the goalkeeper got down well to push away his strike.
Chelsea were threatening to run riot as Ramires’ effort deflected off Keane and onto the crossbar, but against the run of play, Chris Martin forced Schwarzer into a smart save as Derby looked for a way back into the game.
Substitute Mason Bennett also came close as he fired wide with Derby enjoying a good spell of late attacks, but they were unable to breach Schwarzer’s goal and Chelsea headed back to London with their place in the next round safe.
The fourth-round tie against Stoke will now take place at Stamford Bridge on the weekend commencing January 25.