Peter Whittingham doubled the lead after Chris Burke's shot was parried, but Rovers - who were significantly improved after the break - got the nerves jangling thanks to Steve Elliott's strike.
But teenager Josh Magennis secured the Welsh side's path into the third round with his first senior goal late on.
The Bluebirds were on the front foot from almost the first whistle and Chopra had his first effort in the fifth minute but his 25-yarder was off target.
But the chances kept coming for the home side and Gabor Gyepes headed wide before Chopra was again off target from just inside the box.
Gyepes came even closer in the 14th minute when he thumped a header against the post from Whittingham's free-kick.
Full debutant Kelvin Etuhu then came to the fore and fired wide before being denied by Rhys Evans, with Chris Burke sending the rebound over the top.
Etuhu then tried his luck from a tight angle when he might have passed to Chopra, but Evans again denied him.
There was nothing, though, the Rovers stopper could do about Chopra's opener with 33 minutes gone.
Dominic Blizzard was robbed in the centre of the pitch and Whittingham teed up Chopra, who burst into the box, opened his body and curled a right-footed shot home.
Chopra had another effort on the stroke of half-time and Burke shot wide early in the second half but Rovers were much improved after the break and Chris Lines headed their first real chance wide.
But the Bluebirds doubled their advantage in the 66th minute when Etuhu broke and found Burke, whose shot was parried by Evans and Whittingham followed up to score.
Gavin Rae was denied by Evans as the Bluebirds continued to press before the lively Etuhu shot wide again from a Whittingham corner.
However, Rovers grabbed a lifeline 15 minutes from time when Stuart Campbell's corner found Elliott and his effort went in despite the best efforts of Peter Enckelman.
And they soon had a chance to draw level when David Pipe found himself with time to shoot in the area, but he fired over the top - and it was game over five minutes from time.
Paul Quinn overlapped on the right and crossed for Chopra who headed towards goal, Magennis getting the final touch.