Rovers exacted their revenge for an opening day 3-0 defeat on the south coast, which also included a missed spot-kick from the home side, as they put the disappointment of a European exit firmly behind them.
David James endured an afternoon to forget - at fault for both of Nonda's opening goals in the first half - before giving away a penalty, which he got up to save from the Rovers striker.
Stephen Warnock had earlier sealed the victory for Mark Hughes' men with his first goal for the club.
Having gone 90 minutes without being able to find that elusive goal in midweek, Rovers needed just 57 seconds to open the scoring at Ewood Park.
Sol Campbell failed to head clear David Bentley's lofted ball over the top and Nonda won the race ahead of James to flick the ball into the empty net.
On 21 minutes, and after giving away a clumsy free-kick, Stephane Henchoz then failed to clear Pedro Mendes' ball in and Lomana LuaLua blasted inches wide of Brad Friedel's right-hand post from inside the box.
And the miss proved costly as, just four minutes later, Rovers doubled their advantage.
Bentley took a quick throw down the right to Matt Derbyshire, the young striker did brilliantly to cross the ball in from the byline, James and Noe Pamarot got in each other's way and Nonda was left with the simple task of sliding home his second of the game at the back post.
Ten minutes later and after some neat interplay between Bentley, Tugay and Morten Gamst Pedersen, the Norwegian looked to pick out Derbyshire in the centre, but when the 20-year-old forward was sent tumbling under the challenge of Linvoy Primus, referee Mark Clattenburg waved away appeals for a penalty.
The remainder of the half petered out with only some silky ball juggling by Hughes on the touchline keeping the home crowd entertained.
Almost as soon as play had resumed after the half-time interval, Rovers were celebrating their third of the afternoon.
A lightening quick break from defence, started by eventual goalscorer Warnock, saw Derbyshire drive at Primus before feeding Nonda on the right.
The DR Congo unselfishly centred for his strike partner, but Warnock won the race to the ball and smashed home his first goal for the club.
Jason Roberts was brought on to add some extra weight in attack and the former Portsmouth loan striker almost grabbed his first goal in a blue-and-white shirt only for James to palm his effort around the post from outside the box.
As the game drew to a close, midfield maestro Tugay led the early celebrations with some trademark party tricks, including a brilliantly disguised through ball to Nonda, who was again thwarted by a fine finger-tip save from James.