Locked at 1-1 after normal time, Chelsea struck twice in the first period of extra-time to take the game beyond a courageous Liverpool in a typically entertaining and full-blooded all-Engish affair.
Drogba put Chelsea in the driving seat at Stamford Bridge just before halftime - and celebrated in front of Liverpool boss Rafa Benitez, who had criticised the Ivorian in the lead-up to tonight's big clash.
On 33 minutes Chelsea made their superiority tell. Frank Lampard's ball sent Salomon Kalou in on the left and his fierce drive was punched away by Jose Reina.
But the went only as far as Drogba. John Arne Riise was not close enough to block the effort and his angled drive thundered past Reina at the near post.
The striker's celebrations were directed at only one man, Benitez, who had caused a storm pre-match with his criticism of the Chelsea man's perceived inability to stay on his feet.
Fernando Torres was barely in the game, such was his lack of service and John Terry and Ricardo Carvalho's display at the back. But after halftime he hauled Liverpool back into the tie.
Yossi Benayoun cut in from the right and beat two defenders before slipping the ball into Torres' path.
The Spaniard found a yard of space to guide home the equalising goal - Liverpool's first goal in nine games at this stadium under Benitez.
Anxiety was all around Stamford Bridge for the hosts after such a commanding performance and it stayed that way until the first period of extra-time.
A lunge by Sami Hyypia ten minutes in left Michael Ballack spread-eagled inside the visitors' penalty area for a clear penalty. Frank Lampard showed incredible poise to slot home the spot-kick.
Then Drogba hit his second just before the break, as substitute Nicolas Anelka cut the ball back from the byeline for him to slot home at the near post.
But Ryan Babel shook Chelsea nerves with a long-range effort just before fulltime. Petr Cech allowed the effort to slip through his fingers and into the top corner.
Chelsea managed to stay strong in the final minutes and Stamford Bridge erupted into celebration as the ref blew for fulltime.
