The Rams went ahead as early as the seventh minute, when Steve Howard did well to hold up the ball under pressure from the Tigers' defence.
He passed the ball to Tommy Smith, who hooked it on to Matt Oakley. Oakley appeared to be more than a shade offside, but the Tigers were to be punished for their hesitancy as they waited for the linesman to raise his flag.
City's defence stood and watched as Oakley latched on to the loose ball and fired in an 18-yard shot which crept under City goalkeeper Bo Myhill.
Derby, buoyed by the early goal, had the better of the possession and chances as the half wore on and were dangerous on the break.
However, Ryan France did get the better of Derby's right-back Richard Jackson, before the unmarked Darryl Duffy was able to drill a low 25-yard shot which was easily held by the Rams' 11th-hour signing Stephen Bywater.
Two minutes later, Myhill parried a curling 20-yard free-kick from Inigo Idiakez.
In the 23rd minute, Seth Johnson headed over from 12 yards from a pinpoint cross by Idiakez, as Derby continued to boss the proceedings. The Tigers were looking increasingly outclassed, with Jon Parkin fighting a losing battle against the strong Rams defence and the lack of service from his own players.
In the 41st minute, as Derby pressed forward again, Giles Barnes should have done better as he volleyed over from a long-range free-kick by Seth Johnson.
With seconds of the first half remaining, City were gifted an equaliser. Craig Fagan, who had been largely shut out of the game down the right wing, was cynically felled by Paul Boertien just inside the area.
Parkin made no mistake with the resulting penalty, placing a right-footed shot past Bywater in the bottom right-hand corner of the net.
It was a blow to Derby, who seemed to lose their way somewhat in the second half.
After the restart, the Tigers came out showing significantly more drive and purpose than they had in the previous half. A dangerous free-kick from Dean Marney on the left caused problems in Derby's defence and only just went out of play in the 47th minute.
In the 61st minute, the Tigers pressed forward again, showing a coherence and determination largely absent in the first half, and David Livermore drilled a 20-yard shot past the right post.
Smith had a golden chance to get Derby's second in the 70th minute, when City's defence was split in two and he was left unmarked 18 yards out, but his tame shot was easily held by Myhill.
But he was gifted a chance to redeem himself seconds later, putting a unconvincing penalty past Myhill after the linesman controversially ruled Sam Collins to have handballed in the area.
Collins, whose protestations earned him a booking for unsporting behaviour, had not raised his hand, the ball merely glancing off his arm.
Parkin did extremely well to turn and fire in a shot from just outside the box a few minutes from time, but Bywater was up to the task and held on comfortably.
A frenetic last few minutes ensued as City scrambled to get back on terms, but it was Derby who were calm under pressure and went home with all three points and the match officials were booed off the pitch by the 15,000 home supporters.