Peter Whittingham began the rout and Chris Burke netted City's other goal as the Bluebirds put the visitors to the sword.
Rob Hulse did briefly put his side back in the game straight after the break but City were unstoppable in front of goal.
There was only one change in the Cardiff line-up with Stephen McPhail replacing the suspended Joe Ledley in midfield.
Former Wales international Robbie Savage skippered a Rams side with only one point from their travels this season.
Jay Bothroyd raced down the left flank twice in the opening five minutes but his crosses came to nothing.
The Bluebirds went ahead in the tenth minute when Bothroyd raced on to a Mark Kennedy's pass down the right. He drew Stephen Bywater before sliding a pass to Whittingham who side-footed home from two yards.
City doubled their lead with a simple goal in the 36th minute. Kennedy received the ball from Bothroyd and crossed into the danger area where Chopra was waiting to fire into the net.
Derby pulled a goal back two minutes after the re-start when the Bluebirds failed to clear a Gary Teale corner and Hulse stuck out a foot to prod beyond David Marshall in the home goal.
City restored their two-goal advantage in the 57th minute when Burke fed Chopra who shot across Bywater and into the far corner of the net.
Five minutes later Chopra completed his hat-trick when McPhail put him through and he calmly lobbed Bywater to put the ball into an empty net.
Straight from the kick-off. the Bluebirds added to their lead when Burke ran through and fired home.
Derby looked a shattered outfit and they were undone yet again by another pass from McPhail to Chopra who raced on to slam in his fourth and City's sixth goal of the game in the 75th minute.
Cardiff Official website
Derby Official website