Two weeks after a shock 4-2 defeat by Manchester City at Stamford Bridge, Chelsea rediscovered their form and with Florent Malouda enjoying one of his best games for the club ended up handsome winners.
Drogba's double and one for Malouda killed off relegation-threatened West Ham who were level at halftime after former Chelsea man Scott Parker cancelled out Alex's header.
Nicklas Bendtner, fresh from a Champions League hat-trick against Porto in midweek, punished Hull keeper Boaz Myhill's mistake in the third minute of stoppage time to earn Arsenal a 2-1 victory at 10-man Hull.
Below the title scrap, Roman Pavlyuchenko boosted fourth-placed Tottenham Hotspur's push for Champions League qualification with two goals in a 3-1 home defeat of Blackburn Rovers.
Aston Villa, one of Tottenham's rivals for fourth spot, lost ground with a 0-0 draw at Stoke City.
Carlo Ancelotti's side produced just that to outclass a West Ham side, managed by former Chelsea favourite Gianfranco Zola, who hung on gamely for a while after Parker's superb equaliser.
"Malouda was the best player on the pitch today and scored a fantastic goal," Ancelotti told Sky Sports. "He's in a very good moment and I want him to play like that on Tuesday (and) he won't play left back (like he did in the first leg)."
While the free-flowing 5-0 demolition of Porto was one for the purists, against a tenacious Hull side Arsenal proved they can mix it on football's battlefields.
Andrei Arshavin put the visitors ahead but Jimmy Bullard's penalty after Sol Campbell bundled over Jan Vennegoor of Hesselink looked set to give Hull a valuable point despite them having George Boateng sent off in the first half.
