Ivory Coast captain Drogba appeared to have finally killed Liverpool off when he turned in a cross from Nicolas Anelka with pinpoint precision after 105 minutes.
But Liverpool, five times European champions, winners under coach Rafa Benitez in 2005 and beaten finalists last year, never gave up and got an unlikely reprieve with Babel's goal.
That, though, was their last hurrah as Chelsea held on to celebrate an epic win in front of their delirious fans.
"It is something amazing," said Drogba. "I think today we played very well -- I am really pleased for the club because we have been looking for this final for too long.
"Today what we achieved is fantastic for the fans."
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