Manager Carlo Ancelotti's side took full advantage of nearest title rivals Manchester United's 3-1 defeat at Everton earlier in the day to move a step closer to the championship crown.
Chelsea had to wait, though, until the 40th minute before breaking the deadlock against relegation-threatened Wolves at Molineux, with Drogba capping a brilliant move involving Yuri Zhirkov and Michael Ballack.
Drogba then wrapped up the victory in the 67th minute with his 25th goal of the season, and his sixth in five matches since he returned from African Nations Cup duty.
Arsenal continue to hang on in the title race after a 2-0 win at the Emirates Stadium over Sunderland, who remain without a victory since the end of November.
Nicklas Bendtner's first goal for almost four months gave Arsenal the half-time lead, although Kenwyne Jones missed a glorious one- on-one chance shortly before the break to send the sides in level.
Cesc Fabregas added a second late on from the spot to ensure the Gunners remain six points behind Chelsea and two adrift of United with a game in hand on the latter.
In the relegation battle at Upton Park, West Ham are four points clear of the drop zone following a 3-0 victory over 10-man Hull.
The Hammers dominated throughout, taking the lead after just 130 seconds when Valon Behrami scored his first goal for the club for just under 13 months.
After the interval Hull then had a player sent off for the second successive away match when Craig Fagan was dismissed in the 53rd minute for a second bookable offence.
Six minutes later Gianfranco Zola's side took full advantage with Carlton Cole strengthening his claims for a place in England's World Cup squad with his ninth goal of the season before Julian Faubert wrapped up the scoring in the third minute of injury time.
At Goodison Park, United missed the chance to stay in touch with Chelsea as Sir Alex Ferguson's side suffered their sixth league defeat of the season.
United grabbed a 16th-minute lead when Dimitar Berbatov cracked home his ninth goal of the campaign with a right-foot drive off the underside of the crossbar from seven yards.
It was an advantage, though, that lasted just two minutes and 40 seconds as Edwin van der Sar was given no chance by a stunning 20 -yard left-foot swerving shot from Diniyar Bilyaletdinov.
Everton's youngsters in 20-year-old Dan Gosling and 18-year-old Jack Rodwell then stole the show with goals in the 76th and 90th minutes respectively after both had come off the bench in the second half.
Stoke substitute Salif Diao snatched a last-gasp 2-1 triumph for the 10-man Potters as Portsmouth were plunged deeper into the relegation mire.
Frederic Piquionne gave the home side the advantage after 35 minutes, but Robert Huth's header levelled matters five minutes after the break.
Andy Wilkinson was sent off for the visitors after 73 minutes, but Diao netted at the death to maintain his side's unbeaten record in all competitions this year.