Fulham appeared to have tired legs following their midweek exploits as Nonda grabbed his first Ewood Park goal and McCarthy netted his eighth of the campaign.
Rovers boss Mark Hughes was forced to make two changes to the side that last played away to Feyenoord in the UEFA Cup. Captain Lucas Neill returned in place of the suspended Tugay, while Stephane Henchoz was handed his second successive league start in place of the injured Zurab Khizanishvili.
Former Rover Chris Coleman made four changes following Wednesday night's surprise 2-1 victory over neighbours Arsenal. Heidar Helguson and Collins John were preferred to goalscorers Brian McBride and Tomasz Radzinski in attack, Ian Pearce returned from suspension in place of Philippe Christanval, whilst Jan Lastuvka was handed a first league start in place of the injured Antti Niemi in goal.
Fresh from a nine-day break, Rovers started the game at a blistering pace and took the lead with less than six minutes on the clock. Henchoz played a perfectly-weighted pass over the top to Nonda and the Congolese captain diverted the ball past the wrong-footed Lastuvka with an acrobatic overhead kick.
The home side were in control and threatened again just four minutes later. After neat interplay in the centre, McCarthy found Neill on the right and from the Australian's deep cross Morten Gamst Pedersen got up well but headed wide of the mark.
Robbie Savage was booked for a foul on Michael Brown on 18 minutes, before Nonda appeared to have his shirt pulled by Papa Bouba Diop in the area, but amidst appeals from only the home fans, referee Steve Bennett waved play on.
But just five minutes later, Rovers further stretched their lead. Andre Ooijer picked out McCarthy with a long ball from the back, the South African star chested the ball into his path, turned brilliantly inside Pearce, before his right-foot shot looped off the former Rovers defender and into the top corner of the goal.
Rovers continued to dominate with Brett Emerton firing straight at Lastuvka under pressure from Liam Rosenior, before the Fulham full-back unnecessarily headed the ball behind his central defensive duo and Pedersen stole in to volley wide of the right-hand post.
Fulham's best and virtually only chance of the half arrived just minutes before the break when Claus Jensen found Helguson with a volleyed through ball, but the Iceland international's shot finished closer to the corner flag than Brad Friedel's goal.
Rovers almost extended their lead with the move of the game 11 minutes into the second half. After an excellent exchange of passes between Aussie duo Emerton and Neill, the Rovers skipper was denied the goal of the game by the legs of Lastuvka.
Pedersen fired well wide following a corner from the right on the hour, before McCarthy turned inside Rosenior to fire straight into the arms of the keeper.
The former Porto man should have made the points safe after Emerton picked him out unmarked in the area, before Friedel preserved a clean sheet with an outstanding left-hand save on 87 minutes following Jensen's curling free-kick through a crowd of players.