Mark Kennedy failed a late fitness test but Paul Quinn was fit to resume at full-back to replace the suspended Tony Capaldi.
Robins striker Nicky Maynard had an early shot on goal but he spooned his effort and David Marshall was able to gather.
Eight minutes in, Danny Haynes got the better of Paul Quinn down the right flank but Mark Hudson made a superb block on Maynard from in front of goal.
The Bluebirds were finding it difficult to settle but Chris Burke did work his way round keeper Dean Gerken in the 13th minute only to delay his shot and the chance was lost.
Four minutes later Joe Ledley was denied by Gerken as he homed in on the Robins goal.
The Bluebirds took the lead in the 36th minute when a teasing cross from Adam Matthews was turned into his own net by Robins skipper, Jamie McCombe.
Straight from the kick-off, the visitors roared back and Haynes struck the post from close range with Marshall beaten.
On the stroke of half-time, the Bluebirds doubled their lead with a superb goal from Chopra. Burke made all the running through the centre evading tackles before releasing Chopra who finished clinically for his seventh goal of the season.
The Robins threw on an extra striker at the start of the second half in an attempt to claw themselves back into the game.
A free-kick from Jamie McAllister was fumbled by Marshall but he gathered at the second attempt.
Anthony Gerrard went off to have a cut to his head stitched and the Bluebirds played on with ten men until he reappeared four minutes later.
City went three up after 65 minutes and once again it was Burke who caused havoc in the visitors defence. He cut in from the right before sending Rae racing through the middle to fire into the corner of the net.
New loan signing Kelvin Etuhu replaced Chopra in the 78th minute as the Bluebirds remained on top until the final whistle.