Drogba scored with a superb left-foot strike, three minutes before half-time, but the Blues had to play most of the second half at Stamford Bridge with 10 men.
Michael Ballack was sent off for stamping on Mohamed Sissoko's knee in the 52nd minute.
The win puts Chelsea eight points clear of Liverpool, although the Merseysiders have played a game less.
Ballack's red card was the main flashpoint in another fiery game and almost overshadowed a brilliant goal from Drogba.
Frank Lampard hoisted a long pass towards the Ivory Coast striker from the Chelsea right.
Drogba controlled it on his chest, with his back to goal and Jamie Carragher tight behind him.
Then he spun in a flash and unleashed a half-volley which hit the net before keeper Jose Reina had moved a muscle.
Roman Abramovich and Tiger Woods applauded from their seats in the West Stand but Mourinho stayed in his seat, nodding approvingly.
Mourinho was soon on his feet though and, in fact, on the pitch, demanding a red card for Sissoko.
The Liverpool midfielder had just been booked for a foul on Claude Makelele when he mistimed a sliding tackle on Lampard in first-half stoppage time.
It brought a promising Chelsea counter-attack to a halt and the Blues were angry.
Referee Mike Riley gave a free-kick but chose not to show Sissoko a second yellow card.
The significance of this decision was brought into sharper focus after the break when Ballack was dismissed for a foul on Sissoko.
Sissoko, under pressure from Lampard in midfield, stretched his right leg out to pass the ball.
Ballack arrived as the pass was made and sank his studs into the knee of the Liverpool midfielder.
It did not seem malicious and maybe not intentional but he certainly stepped onto his knee.
It was right in front of Riley and the ref had no hesitation in pulling out his red card.
The game had erupted after starting in such a friendly spirit.
Managers Mourinho and Rafael Benitez patched up their differences before kick-off with a pre-match handshake.
Daniel Agger produced a brilliant goalline clearance to stop Chelsea taking an early lead.
Ricardo Carvalho collected a deep free-kick from Lampard and lifted the ball back into the goalmouth.
Ballack headed it across goal and Andriy Shevchenko and Reina challenged for the ball.
Reina could only punch it up in the air and John Terry came charging in to try to bundle the ball over the line.
Agger managed to twist and stretch out a leg to hook it clear and Terry landed awkwardly in the back of the net.
The England captain continued after lengthy treatment.
Liverpool responded well and Dirk Kuyt smashed a shot against the crossbar when he was found in space by Xabi Alonso's pass.
Peter Cech was beaten by the power of Kuyt's effort but breathed a sigh of relief as it rebounded to safety. Reina smothered a firm free-kick from Lampard in the 20th minute and then gathered easily as Shevchenko tried a left-foot volley from the edge of the box.
Shevchenko, who invited Woods to the game after meeting him at Wentworth Golf Club in Surrey last week, has yet to find top form since his £30million move from AC Milan.
The Ukrainian was eventually sacrificed as Mourinho reshuffled his team after Ballack's sending off.
Arjen Robben, back after a calf injury, replaced him for the last 25 minutes and caused problems with his pace on the counter-attack.
Robben was immediately tripped by Sissoko and the Stamford Bridge crowd were baying for the Liverpool midfielder to follow Ballack down the tunnel.
Benitez spotted the danger and replaced the midfielder with Boudewijn Zenden.
Robben was felled under a pincer tackle from Carragher and Agger. The Blues wanted a penalty but Riley waved play on.
Steven Gerrard became more influential against Chelsea's depleted midfield but missed Liverpool's best chance.
He wriggled clear of Khalid Boulahrouz but drilled his shot straight at Cech.
Kuyt glanced a header wide and lifted a shot over as the visitors finished strongly.
Peter Crouch was denied by the faultless Cech and Chelsea hung on through five minutes of added time.
Charlton 0-1 Portsmouth
Bolton 0-0 M'brough*
Everton 2-2 Wigan
Sheffield Utd 1-2 Reading
Watford 0-0 Aston Villa*
Sun., Sep. 17
Blackburn 4-2 Man City
Chelsea 1-0 Liverpool
Man Utd 0-1 Arsenal*
Tottenham 0-0 Fulham
West Ham 0-2 Newcastle
Ballack was sent off for a stamp on Liverpool's Mohamed Sissoko in the 52nd minute of Chelsea's 1-0 win at Stamford Bridge on Sunday.
Referee Mike Riley showed him a red card for violent conduct.
Clubs are entitled to appeal against all straight reds but must register their intentions before 1pm on the day after the game.
Blues boss Jose Mourinho had no complaints about the dismissal after the game and Ballack apologised to Sissoko after he watched a television replay of the incident, admitting "it didn't look good".
The deadline for an appeal has passed and the Football Association have not heard from the champions.
Ballack, 29, will miss games against Fulham, Aston Villa and Reading.
He can play in the Champions League against Levski Sofia next week and will be available for domestic action against Portsmouth on October 21.
The plaintiff's lawyer, Jean-Louis Dupont, said Monday that betting companies like Bwin, Unibet and William Hill "use without any authorization their names and insignia for purely commercial gain."
The court proceedings opened in eastern Liege on Friday and are expected to take several months.
Dupont claimed that the betting companies aren't legally authorized to work in the European Union. He also said the clubs - which includes PSV Eindhoven - have already lodged a similar lawsuit in Paris.
PSV spokesman Pedro Salazar said the Belgian lawsuit would act as a test-case on the issue.
"Our rights are used and abused to allow them to make lots of money," he said.
Source: Fox Soccer
Woot for Arsenal, well done
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