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.
It left Chelsea and Arsenal locked together on 64 points although the leaders have a better goal difference and a game in hand.
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.
Burnley look increasingly likely to make a quick return to the Championship fter a morale-sapping 2-1 home defeat against fellow strugglers Wolverhampton Wanderers.
Bolton Wanderers thrashed Wigan Athletic 4-0 and Birmingham City recovered a two-goal deficit to draw 2-2 with Everton.
COMMANDING PERFORMANCE
Chelsea needed a commanding performance as they looked forward to welcoming former manager Jose Mourinho back to Stamford Bridge on Tuesday when they seek to overturn a 2-1 deficit against Inter Milan in the Champions League.
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, in dazzling form down the left wing, provided the cross for Brazilian Alex to score the opener and set up Drogba to head Chelsea back in front soon after the interval.
Frenchman Malouda then made it 3-1 after a dribble and shot before Drogba bagged his second in the final minute.
"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)."
Kicking off in the evening on a rutted Hull pitch Arsenal knew victory was essential.
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.
Hull resisted everything Arsenal threw at
