Chopra had the first shot in the fifth minute but it flew just wide of the post as City passed the ball around neatly in the wet conditions.
When Chris Burke was fouled down the right corner ten minutes later, his free-kick was headed against the post by Gabor Gyepes. Shortly after, Etuhu left the field for attention to a facial injury but returned after five minutes to see Chopra shoot just wide once again.
The Bluebirds had continued where they left off on Sunday with some delightful football but midway through the opening half they had managed very little on target until Etuhu broke free and forced a fine save from Rovers keeper Rhys Evans.
Jo Kuffour was proving to be a handful up front for the visitors but with City controlling the game, he was given little opportunity.
The Bluebirds scored the goal they deserved when persistence from Etuhu saw the ball run free to Chopra and he fired home his eighth goal of the season on the half-hour.
No changes for either side after the break and City won a corner in the opening minute but Burke fired wide.
The Bluebirds were content to keep passing the ball around but there seemed little urgency in their play until Whittingham popped up in the 65th minute to slot home after the Rovers defence failed to clear a Burke cross.
Ten minutes later Rovers pulled one back when Steve Elliott headed home a Stuart Campbell corner.
The Bluebirds made the game safe five minutes from time when Magennis headed in from close range after Burke had crossed from the right flank.