The luckless Argentinian, making only his second start of the season after being sidelined by a pelvic injury, stretched to cut out Sean Davis' right wing cross under pressure from Fulham sub Louis Saha - but could only divert the ball past goalkeeper Mart Poom.
The Rams could have equalised in almost identical fashion two minutes later when Francois Grenet's cross was deflected around his own post by visitors' captain Andy Melville.
But Fulham deserved a lead which returning front man Steve Marlet ought to have given them earlier.
Marlet, the £11.5million man making his first start in two months after a knee injury, wriggled behind the Rams defence in the 56th minute but hit a close-range shot straight at Poom.
And on 69 minutes he had an even better chance when he failed to control
Davis' cross and fluffed his chance from six yards.
Derby, anxious to build on Saturday's first away win of the season, had struggled throughout, the best chance of their own making falling to in-form striker Malcolm Christie.
Christie, who had scored the winner at Ewood Park, bundled the ball over the bar from 12 yards after Luciano Zavagno's 38th minute cross from the left had eluded the Fulham defence.
Fulham had been the better team from the off, with Steed Malbranque bringing a good save out of Poom in the second minute and Barry Hayles shooting tamely at the keeper after being put through 10 minutes later.
Then Darryl Powell caused panic in the Fulham box with a high ball over his head, but as goalkeeper Edwin van der Sar punched off his line under pressure from Fabrizio Ravanelli, referee Barry Knight blew for offside.
Fulham boss Jean Tigana had responded to his side's home defeat to Manchester
United on Sunday by dropping Saha and Luis Boa Morte from his front line but the former, with only one goal in four months, replaced Hayles in the 65th minute.
And he could tenuously claim to have had a say in the winning goal after putting Carbonari under some degree of pressure in the box.
Fulham held out as Derby threw men forward, their only breathless moment coming when Dutch stopper van der Sar elected to dribble clear under pressure from home sub Deon Burton, and eventually had to bundle the ball out for a corner.
Christie saw late claims for a penalty turned down after he fell under a challenge from Melville.
Saha should have made the points safe in the 89th minute when Davis again crossed from the right.
The striker found himself in the clear but denied by another excellent save from Poom.