Blackburn went into the break a goal down despite a terrific first-half performance against Chelsea.
Joe Cole's strike separated the sides. The England winger latched onto a pass from Kalou, and finished a surging run with a 20-yard strike into the top left-hand corner.
Earlier, Carvalho, starting his first league game since November 11, made a crucial block in the fourth minute, flinging his body in front of a rasping drive from an in-form Roque Santa Cruz.
From the ensuing inswinging corner by Morten Gamst Pedersen, the ball flew through the six-yard box and inches beyond the far post, with no Rovers player able to conjure a decisive touch.
Then David Bentley shaved the bar with a rising drive from the edge of the area two minutes later.
Then Bentley went close to opening the scoring with a curled right-foot effort that struck the top of the bar.
With Rovers on top they again failed to take advantage in the 13th minute as a superb ball from Bentley into Santa Cruz culminated in the Paraguay striker ending up inches wide with an angled right-foot shot from 16 yards.
Brad Friedel touched a Frank Lampard shot onto the post just before the break.
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