Dominant Chelsea reclaimed top spot in the league and heaped more pressure on relegation-threatened West Ham.
Florent Malouda crossed for Alex to open the scoring for Chelsea with a powerful header from six yards.
But the Hammers hit back through Scott Parker who unleashed a vicious half-volley over the head of Ross Turnbull.
Another Malouda cross found Drogba whose header put Chelsea back in front before Malouda coolly slotted a third and Drogba tapped in the fourth.
From the start West Ham defended deep against title-chasing Chelsea - perhaps unsurprisingly considering they started the day only three points outside of the bottom three.
But the Hammers should have taken the lead early on.
Jonathan Spector outmuscled Paulo Ferreira on the by-line and the lose ball fell to Mido who squared to Ilan, unmarked on the edge of the six yard box, but the Brazilian hammered his effort over the bar.
Chelsea's formidable home record, consisting of only defeat by Manchester City this season, has not been a product of handing chances to opponents and Carlo Ancelotti's side waited just two minutes to punish the Hammers' profligacy.
Malouda, in an acre of space on the left, produced an inch-perfect cross which defender Alex powered past Green to open the scoring.
Chelsea almost made it 2-0 moments later courtesy of another cross from the lively Malouda.
This time struck the ball arced over Nicolas Anelka's head and struck the thigh of Matthew Upson before looping over the back-pedalling Robert Green and clipping the crossbar.
But if Chelsea, who knew a win would take them top of the Premier League, thought the game would go all their way they were mistaken as Zola's well organised side harried and pressed their West London rivals.
And eventually the Hammers tenacity was rewarded.
Kieron Dyer's throw in, which television replays suggested was a foul throw, was flicked on by Jon Obi Mikel and bounced kindly for Parker.
The former Chelsea man, who left Stamford Bridge for Newcastle in 2005, took one touch before launching a looping right-footed half-volley beyond Turnbull and into the top right corner - for the midfielder's first goal of the season.
That was to be as good as it got for West Ham who, despite no lack of effort, were overpowered by Chelsea.
The main source of danger for the home side was Frenchman Malouda, who continued to torment Spector.
Chelsea's second goal came from a piece of John Terry-inspired attacking play.
The former England skipper dribbled the ball out of his own half charged towards the 18-yard box before finding Drogba who slipped the ball out to Malouda.
The Frenchman returned the compliment by placing another impeccable cross onto the head of the Drogba who doubled the lead.
As Chelsea threatened to add another it gave Rob Green, playing his 116th successive league game, the opportunity to impress the watching England boss Fabio Capello.
And Green did that when another Chelsea cross found Alex who saw the England goalkeeper palm the ball around the post at full stretch.
With the introductions of Joe and Carlton Cole in the second half the England manager will also have had the opportunity to see a fair proportion of his potential World Cup squad on show - although neither Cole had much of a chance to impress.
Malouda finally added the goal his endeavour deserved when Drogba controlled a long ball and laid it off to the winger, who coolly passed his finish beyond Green.
Lampard hit the post from Malouda's cross as Chelsea threatened to give the score a slightly unfair edge but West Ham could not hold out for long.
After finding space Lampard struck another fierce effort, this time spilled by Green, which fell to Drogba who snatched his 27th goal of the season.
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