|
Roger Johnson's first-half header was ably supported by strikes from Gavin Rae, Jay Bothroyd and substitute Eddie Johnson after the interval.
But American striker Johnson turned from hero to zero when he sliced Gary Teale's stoppage-time corner into his own net.
The result sees the Bluebirds leap above Burnley into fifth place in the Championship table but the scoreline flattered the hosts after Derby had dominated the opening half.
Johnson set the hosts on their way with a 16th-minute header before quick-fire second-half strikes from Rae and Bothroyd and a fourth from Johnson sealed a convincing victory.
Cardiff boss Dave Jones made three changes following the pulsating south Wales derby draw with Swansea City last Sunday.
Bluebirds skipper Joe Ledley was rested allowing Stephen McPhail to regain the captain's armband with Rae restored to central midfield.
Gabor Gyepes, fresh from signing a three-year contract extension, and Peter Whittingham also started as Darren Purse and Paul Parry made way.
Rams manager Nigel Clough opted to make just two changes with John Eustace and Mile Sterjovski replacing Kris Commons and Stephen Pearson.
The visitors started brightly and, within 90 seconds of the kick-off, had a penalty appeal turned down when Eustace appeared to be hauled down by Gyepes.
Derby continued to dominate the early possession and it was the former Coventry midfielder who came closest to breaking the deadlock in the ninth minute.
The hosts failed to deal with Jay McEveley's cross from the left and Eustace's acrobatic volley forced Stuart Taylor to turn the ball around for a corner.
Clough's men kept pressing for the opening goal and should have been awarded a penalty on 14 minutes when Mark Kennedy handled Eustace's powerful shot from the edge of the box.
But two minutes later, Johnson's glancing header past Stephen Bywater put Cardiff ahead against the run of play.
Whittingham floated a fine free-kick in from the right which allowed centre-back Johnson to rise highest to score his fifth goal of the season.
Michael Chopra stung the hands of Bywater before Derby hit back in the 22nd minute when Sterjovski steered his close-range shot wide.
After an action-packed opening quarter, the pace and intensity dropped as both sides failed to create another clear-cut chance before the interval.
Eustace came closest for Derby after the interval before the hosts doubled their advantage when Rae scored his first goal of the season on 61 minutes after latching onto McPhail's slide-rule pass to round Bywater.
Cardiff had their tails up and they grabbed a third goal just two minutes later when Bothroyd prodded Whittingham's corner home.
Derby were left shell-shocked but their woes continued with just 11 minutes remaining when the hosts added a fourth.
Johnson sealed the victory when he broke clean through before coolly slotting the ball past Bywater from the edge of the area to spark wild celebrations among the home fans.
But Derby added a late consolation in stoppage time when Johnson miscued into his own net from Teale's left-wing corner.