The Addicks had the best chance of the opening minutes when the ball fell to Johnnie Jackson and Lee Grant was forced into action to parry the midfielder's goal-bound effort away.
The Rams took the lead in the 18th minute when Patrick Bamford found space in the penalty area and cut the ball back to Johnny Russell, who found the back of the net with a low effort.
The home side began to up the ante as Russell and Jeff Hendrick missed chances from distance, while minutes later Ben Hamer kept Charlton in the contest as he managed to turn over another effort from George Thorne.
Derby did doubled their lead just before the break when Bamford capitalised on an error in the Charlton defence, as he raced onto a weak back-header from Jackson and slotted the ball past Hamer.
After the break, the visitors pressed to get back into the game. Grant was forced into making a good save to deny Callum Harriott after Derby had failed to clear their lines from a cross into the area.
Minutes later, Grant made another good stop to deny Joe Pigott, whose low effort looked to be creeping into the corner before the keeper got a hand to the ball to turn it away.
Derby held out the onslaught from the visitors and sealed the game when Chris Martin headed home Craig Bryson's cross in the 84th minute.