Perhaps Dave Jones' side could not have asked for better opposition to kick-start their home fortunes - Derby arrived having lost seven of their last nine away league games.
Chopra had gone six matches without a goal but helped himself to a second-half hat-trick having added to Peter Whittingham's opening strike before the break. Chris Burke scored Cardiff's other goal.
Rob Hulse's reply soon after half-time to make the score 2-1 proved little more than a consolation.
Whittingham's opening goal was a controversial one. Jay Bothroyd looked to be offside as he raced clear of the Derby defence before Whittingham had the simple task of converting his right-wing cross from close range.
The Rams responded well to the early setback but Nigel Clough's side were kept at arm's length by City. Fredrik Stoor's shot from 20 yards went wide before Lee Hendrie had two efforts from a similar range blocked by Anthony Gerrard and Mark Hudson.
But Cardiff's strike pairing of Bothroyd and Chopra had been causing the Derby defence all sorts of problems with their pace and movement, and the latter extended City's lead after 36 minutes.
Again there was a suspicion of offside as Whittingham crossed from the left for Chopra to score.
Cardiff then threatened to race out of sight as Stephen Bywater was forced to produce a couple of fine saves just before the break to keep County in the game.
Chopra almost scored his second goal in as many minutes but Bywater tipped his shot round a post. The Derby keeper then parried Bothroyd's effort two minutes later.
The importance of Bywater's saves was highlighted just 90 seconds into the second half when Derby scored to half their deficit.
Hendrie played the ball in to Hulse from the right and the big striker managed to poke a shot beyond David Marshall.
It started to look like the Rams would get back into the game and Hulse had another chance from a header in the 52nd minute
However, just five minutes later Chopra restored Cardiff's two-goal lead. Burke's beautiful backheel wrong-footed the Derby defence and Chopra beat Bywater with a low shot from 12 yards.
Marshall tipped a long-range effort from Hulse over the crossbar on the hour mark before City struck twice in as many minutes to quickly extend their lead to 5-1.
Chopra completed his second hat-trick of the season after 62 minutes with a lovely lob from the edge of the area after latching on to Stephen McPhail's pass.
McPhail then put Burke through seconds later and the former Rangers midfielder finished confidently.
Chopra scored his third goal of the half and completed the rout after 75 minutes, running on to another McPhail pass and clinically firing the ball into the bottom corner.