The Lilywhites opted to relieve Ferguson, the son of Manchester United boss Sir Alex, of his duties after finding themselves languishing at the bottom of the Championship at the halfway point of the season.
That left David Unsworth to pick up the pieces as caretaker manager and he got off to a poor start on New Year's Day as Chris Porter's second-half double overshadowed Callum Davidson's late consolation to ensure the Rams ended a five-match losing run by claiming the points.
Unsworth, who took temporary charge on Thursday, was quick to stamp his authority on North End, making seven changes to the side which fell to a 3-1 defeat against Middlesbrough on Tuesday.
Derby, meanwhile, have endured their own struggles recently with manager Nigel Clough berating many of his players in the wake of Wednesday's 5-2 derby hammering to Nottingham Forest.
And their lack of confidence was evident throughout the opening exchanges as the hosts dominated.
Preston could have taken an early lead through Chris Brown but, after Keith Treacy's initial effort was blocked, the striker scuffed his effort.
As the game wore on energetic winger Treacy, who was deployed as a striker, began to have an increasing influence. He sent over a pin-point free-kick, which Davidson was unable to convert, before firing inches wide.
After weathering the storm, the Rams started to come back into the game midway through the opening period with Conor Doyle hitting just over.
That seemed to open the game up and the Lilywhites had an excellent chance of their own moments later.
Sean St Ledger sent in an excellent centre, allowing Brown to rise highest and head back across goal, only for the ball to elude Paul Parry, who would have been left with the easiest of finishes.
The procession of chances continued, but Unsworth could only watch on in frustration as his side continued to search for a cutting edge in front of goal.
They were almost made to pay the ultimate price on the stroke of half-time as Porter spurned an excellent chance despite being clean through.
Whatever Clough said to his troops at the interval clearly got through, with Derby showing much more vigour in the second period.
Kris Commons came agonisingly close to putting them ahead when he fired just over, before Stephen Pearson saw his curling effort go just wide.
However, they got the reward their endeavour deserved in the 65th minute when the ball rolled to Porter on the edge of the area, allowing him to fire home.
The home side tried desperately to get back into the game thereafter, but Porter fired home from 12 yards to wrap up the points for the visitors.
Davidson pulled one back from the spot after Robbie Savage handled, before Treacy endured the agony of seeing his effort cleared off the line in the dying seconds.