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Charlton almost produced an immediate response as Astrit Ajdarevic's acrobatic effort sailed wide, but there was a let-off for them moments later when Marcus Olsson went clean through on goal only to produce a glaring miss.
The Addicks were handed a lifeline one minute before half time when Marvin Sordell drew a foul in the penalty area and the referee pointed to the spot.
Sordell stepped up to take the penalty himself, but directed his effort straight at Rovers keeper Paul Robinson, leaving his side trailing at the interval.
Things went from bad to worse for Charlton early in the second half when Michael Keane nodded home following a corner, but Sordell made amends for his penalty miss by finding the net minutes after play had restarted to put the hosts back in it.
The goal fired Charlton up, and they looked odds on to net an equaliser after pulling one back, but Tom Cairney crushed their resistance just after the hour mark with a left-footed strike from inside the box.
Jose Riga's side refused to lie down, but they almost fell further behind in the 66th minute as Gestede leaped high to meet a corner, his header coming crashing back off the crossbar.
Sordell almost pulled another goal back with four minutes remaining, but he could only direct his shot wide, leaving Blackburn's two-goal cushion intact come the final whistle.