Karkouri, signed for £1million from Paris St Germain as a defender, was pushed forward by manager Alan Curbishley to add some strength to the midfield and the Moroccan international came up trumps four minutes into the second half when he lost his marker to head in Danny Murphy's corner.
A minute earlier he had set up an opportunity for Kevin Lisbie but the striker hit his shot across the face of goal.
Blackburn manager Mark Hughes, in his third game in charge, will be delighted with his team's spirited performance that deserved at least a share of the spoils.
He saw his team hit the post, have a shot scrambled off the line and have a penalty claim denied, but the victory lifts Charlton into seventh place in the Premiership despite the fact that they are still not firing on all cylinders.
The game started brightly with Charlton's Graham Stuart, who was making his 500th career appearance, having an early shot deflected for a corner and Garry Flitcroft seeing his close-range effort hit the post and deflect into the path of keeper Dean Kiely.
Charlton lost striker Francis Jeffers after only 12 minutes with a neck injury and his replacement, Jonatan Johansson, saw his early shot hit Dominic Matteo and fly to safety.
After a disappointing first half the second period sprang to life with Karkouri's goal but after they had gone ahead Charlton were forced back by a sustained spell of pressure from the visitors that should have seen them grab an equaliser.
They perhaps should have had a penalty when Hermann Hreidarsson handled a cross in the penalty area but got away with his indiscretion.
Blackburn could have been punished on the break as Charlton twice missed good chances. Brad Friedel made a great save to deny substitute Radostin Kishishev and Lisbie then headed over after good work by another Charlton substitute Jason Euell.
But Rovers continued battling as they looked for a deserved point and Matt Jansen headed wide from an excellent chance.
Curbishley has been critical of his team's inconsistent form this season and they have probably gone back to basics with this performance. He left star Danish winger Dennis Rommedahl on the bench and was without the injured Matt Holland and Shaun Bartlett.
Blackburn, with only one win this season, already look as though they are making progress under Hughes with all the players responding to their new manager, but they will need to take their chances if they are to move up the table.