Goals at the start of each half at the Cardiff City Stadium on Saturday proved too much of a mountain for a poor Rams side to overcome on what was an afternoon to forget for Nigel Clough's side who are far from safe, albeit nine points clear of the bottom three.
Jay Bothroyd's early penalty, his first goal in 11 games, proved the difference in a very ordinary first half.
Dekel Keinan capitalised on some slack marking to head a second at the start of the second period and, after Steven Davies entered his nomination for miss of the season, Paul Quinn added a third and Peter Whittingham a fourth.
The thoroughly deserved victory, Cardiff's first in five games, was blotted only by Robbie Savage's injury-time spot-kick but moves the Bluebirds above Swansea and into third, still four points adrift of second-placed Norwich.
With Mark Hudson (knee) ruled out and on-loan Rams keeper Stephen Bywater ineligible, City boss Dave Jones handed a debut to deadline day loan signing Jlloyd Samuel at left-back while Tom Heaton made his return from a groin injury.
Derby made just the one change - also between the sticks - after Frank Fielding's 93-day stay had expired, Liverpool loanee Brad Jones making his debut.
But the former Middlesbrough man's first task was to pick the ball out of his net as Cardiff broke the deadlock after just seven minutes courtesy of a fairly soft penalty, the impressive Craig Bellamy going over the outstretched leg of Shaun Barker.
Bothroyd needed no invitation to send Jones the wrong way from the spot.
Barring the early penalty, neither keeper had much to do in the opening 45 minutes.
Bellamy and Barker were again involved in the only other opening of note in the 27th minute, the Rams defender clearing a certain second off the line from the Wales international who had worked himself wide around Jones.
County suffered a blow shortly after the half-hour mark with the loss of midfielder Paul Green who was stretchered off with a serious-looking knee injury.
But four minutes injury time only prolonged what was a disappointing first half, with Derby failing to pose any kind of attacking threat and managing just a single tame shot.
The Bluebirds may have needed seven minutes at the start of the first half but they only needed three at the beginning of the second to effectively put the game beyond the visitors.
Israeli centre-back Keinan was allowed to run unmarked and head Chris Burke's outswinging corner past a helpless Jones.
Derby looked to have pulled one back soon after but Davies somehow diverted the ball over from two yards when it looked as if Barker's flick was heading past Heaton.
And Clough's outfit were made to pay within minutes as Quinn converted Whittingham's cross to make it 3-0 from close range.
Matters went from bad to worse for the Rams as Gareth Roberts became the second player to be stretchered off, before Barker also hobbled off due to injury.
Whittingham then grabbed a deserved goal of his own to leave Derby, who snatched a 95th-minute consolation from the spot through Savage, still having won just three times on Cardiff soil in their history.