Whittingham headed home in the 11th minute and a Chopra free-kick put the Bluebirds comfortably ahead before McNaughton's unfortunate injury.
The Bluebirds included loan signing Simon Walton in midfield, while new Dutch striker Iwan Redan was on the bench.
Paul Parry sent a low cross skimming across the Barnsley goalmouth in the third minute as City pressed and a minute later he had Nick Colgan diving low to clutch a venomous 20-yard drive.
Chopra jinked his way into the penalty area before slipping a pass to Steven Thompson but the big striker toe-poked straight at Colgan.
The Bluebirds took the lead their early play deserved when Chopra cut across from the right flank and flashed in a shot that was deflected beyond the far post where Whittingham bravely headed in from an acute angle.
Neil Alexander had to be alert in the 26th minute when he tipped a close-range shot which deflected off the Walton over the top.
Eight minutes before the interval Joe Ledley failed to recover from injury and McNaughton replaced him at full-back.
Just as the first half was coming to a close Chopra made it 17 goals for the season with a superb free-kick that Colgan reached but could not keep out.
Straight after, McNaughton's injury meant a long delay but the half finished with City on the attack.
The Bluebirds continued where they left off in the second period with Willo Flood replacing the unfortunate McNaughton.
It was ten minutes before the Tykes were able to break out of their own half but when they did it took a Kerrea Gilbert block to prevent Marc Richards from reducing the deficit.
They were now building up a head of steam and Alexander again came to the rescue to push away a goal-bound effort from the busy Richards.
He had yet another chance at the far post but a timely intervention from Gilbert forced the striker to head high and wide.
City finally regained controlled in the closing stages to finish with the victory that cements their place in the play-off positions.
External reports
South Wales Echo
Western Mail
The Independent