Four-goal Michael Chopra fired Cardiff back to form in a crushing victory.
Peter Whittingham got the first in an early sign that Derby's offside trap would be exposed, then he set up Chopra for his first strike since August.
Rob Hulse gave the Rams hope straight after the break, before the division's top-scorer Chopra took over, first latching on to Chris Burke's back-heel.
Stephen McPhail set up the hat-trick, a sweet chip, McPhail playing a part in Chris Burke's goal and Chopra's closer.
The Bluebirds had previously lost five of their last six matches in all competitions, an awful run that had seen the early season Championship leaders slip to ninth spot in the league.
But Derby provided the perfect opposition, having lost seven of their last nine away league games.
McPhail made a huge impression on his return from suspension, replacing Wales midfielder Joe Ledley who was banned for the game.
Cardiff manager Dave Jones:
"Chopra's movement and finishing was top class and he showed us all what a good player he is.
"We had a lot of the ball and used it well but results like that don't come very often and we have to enjoy it while we can.
Derby manager Nigel Clough:
"I am very disappointed at the way we let the goals in particularly after getting back into the game straight after half time.
.
Fiorentina 2 - 0 Liverpool
Stevan Jovetic was Liverpool's tormentor as he scored twice in Fiorentina's surprise win over the Reds in their Champions League Group E tie.
The teenager pierced the visitors' offside trap and slotted past Pepe Reina to put his side deservedly ahead.
He added a second when he diverted in a powerful Juan Vargas strike.
Liverpool had chances to get back into the game but Lucas Leiva put a free header high and Fernando Torres skied a close-range volley.
The Reds did not lose away from home in the Champions League last season but were undone by a poor first-half showing and an inspired Viola at the Stadio Artemio Franchi.
Liverpool had also found the net in their previous 21 Champions League matches and their failure to do so against the Serie A side saw them miss out on Bayern Munich's record scoring run of 22 games.
www.bbc.co.uk