Drogba did the damage three minutes before half-time when he collected Frank Lampard's lofted cross on his chest just outside the penalty area, before turning sharply and unleashing a powerful shot which flew into the back of the net.
Liverpool goalkeeper Jose Reina was rooted to the spot, unable to react quickly enough to even attempt to stop the thunderbolt.
Drogba may have grabbed the headlines but the points were secured by a solid defensive display, even though the Blues had to play the final 39 minutes with ten men after Michael Ballack was sent off for stamping on Momo Sissoko.
The afternoon started well for Chelsea when Reds left-back Stephen Warnock scythed down Drogba on the left to earn a fifth-minute yellow card.
A whipped Lampard free-kick on 10 minutes caused mayhem in the Liverpool defence until Daniel Agger produced a brilliant goal-line clearance.
Five minutes later, Liverpool almost scored when a fantastic defence-splitting ball by Xabi Alonso found Dirk Kuyt on the edge of the Chelsea area. The Dutchman smashed a vicious right footer past Petr Cech but the ball ricocheted to safety off the Chelsea crossbar.
Under-fire Lampard produced a trademark free-kick on 25 minutes but Reina was equal to the task and smothered the shot.
A left-foot shot by Andriy Shevchenko was also on target three minutes later, but was not powerful enough to trouble Reina.
An intricate move on 37 minutes, involving Steven Gerrard, Alonso and Kuyt almost paid dividends for Liverpool, but the Dutchman failed to read Alonso's back-heeled pass and the ball rolled through to Cech.
Then came Drogba's moment of brilliance, ensuring Chelsea led at the interval.
Gerrard almost equalised in stoppage-time but a sharp by-line cross went inches wide of the Chelsea goal.
Within six minutes of the restart, Ballack was red carded by referee Mike Riley for his stamp on the right leg of Sissoko.
Liverpool boss Rafael Benitez perhaps sensed Riley might try to even the score and immediately replaced Warnock, already on a yellow card, with Fabio Aurelio.
On 60 minutes the visitors should have equalised when Gerrard skipped free in the Chelsea area, but the Reds captain drilled his shot straight at Cech.
Chelsea boss Jose Mourinho replaced Shevchenko on 63 minutes with winger Arjen Robben. And within seconds, Benitez replaced Sissoko with Boudewijn Zenden.
The spate of substitutions continued with Mourinho beefing up his defence with Paulo Ferreira at the expense of Khalid Boulahrouz on 70 minutes.
With Liverpool pressing, Riley turned down a penalty shout when Gerrard appeared to fall over Lampard in the penalty area on 76 minutes. The follow-up shot by Craig Bellamy was again saved by Cech.
Peter Crouch replaced Bellamy and the England striker should have scored with eight minutes remaining, but missed the target with a header when unmarked six yards out.
Chelsea defended brilliantly in the remaining minutes and ran out deserved victors.