Cardiff wasted no time in taking the lead after a neat one-two on the edge of the are between Chopra and Jay Bothroyd saw Chopra race through on goal and slot the ball home for his fourth in three games.
The same man added the second late on when he smashed the ball past Romain Larrieu and he added a third from the penalty spot with five minutes left to play.
The Pilgrims had something to cheer about late on when former player Tony Capaldi was shown a second yellow card for a handball in the penalty area and Alan Gow stepped up to slot home the resulting penalty.
The Bluebirds looked impressive after their goal and continued to attack Plymouth at pace with Chopra causing the defence all sorts of problems.
Four minutes after the goal Bothroyd nearly got his name on the scoresheet but his firm header from the penalty spot was blocked by Marcel Seip.
Plymouth looked all at sea as a long ball from the back saw Bothroyd race clear of the Pilgrims' defence but Krisztian Timar put a last-ditch tackle in to send the ball wide for a corner kick.
Jamie Mackie had a fine chance to bring the hosts on level terms when a Carl Fletcher shot deflected to Mackie in the six-yard box but he failed to get his shot on target.
The Pilgrims started the second half brightly pinning the visitors deep in their own half.
Mackie almost created a chance for Rory Fallon but after some bright play on the wing his cross was cleared.
A deep cross from Gary Sawyer had Cardiff goalkeeper David Marshall scrambling on his own goalline and but he was able to push the ball over the bar as it looked to loop in at the far post.
The Bluebirds looked to get back into the game as the second period went on and despite being under pressure for long periods nearly doubled their advantage through Chopra.
The former Sunderland man ran through on goal and attempted a deft lob over Larrieu in the Argyle goal but the ball trickled wide of the upright.
Chopra made it two against the run of play with 10 minutes to go when he drilled the ball home from the edge of the area.
The hat-trick came five minutes later from the penalty spot when he sent Larrieu the wrong way to slot the ball home after Marcel Seip had tripped Chris Burke in the area.
Plymouth grabbed a consolation from the spot in the closing stages when debutant Gow stepped up and hammered home the penalty following the handball and resulting sending-off from Capaldi.