It came in the 79th minute after Joe Ledley fired a wicked cross from the left wing in to the danger area. Coventry goalkeeper Andy Marshall was rooted to the spot and Chopra slid in to slot the ball into the bottom corner.
The Geordie striker went close to doubling the lead a few minutes later, but his attempted lob was finger-tipped to safety by Marshall.
Marshall had been the first keeper called in to action in the sixth minute as he rose to gather a Paul Parry cross. Coventry's David McNamee was injured trying to stop Parry and had to leave the field to be replaced by Adam Virgo.
Steven Thompson was brought down on the edge of the area by Elliott Ward in the 16th minute, after a passage of slick passing play from the hosts.
Before the free-kick could be taken Virgo, who had only been on the field for 12 minutes, was carried off on a stretcher.
A corner by Sky Blues' skipper Stephen Hughes was met by Ward midway through the half, but his header was cleared off the line by Kerrea Gilbert.
Cardiff made a swift break just before the interval. Glenn Loovens raced out of defence and slipped the ball out wide to Ledley. He laid it back to Stephen McPhail and his dipping shot was acrobatically turned over by Marshall.
The hosts upped the tempo after the break and Marcus Hall had to head over his own crossbar twice in the opening five minutes.
Twice the rampant Bluebirds were denied as Chopra and Riccardo Scimeca saw goalbound efforts cleared off the line.
After finally breaking the deadlock Cardiff had several chances to make the game safe, with both Kevin Campbell and Luigi Glombard going close.