Chelsea returned to second in the Premier League as they beat bottom club Portsmouth 5-0.
Carlo Ancelotti’s side followed up defeat to Inter Milan in the Champions League with a draw at Blackburn Rovers on Sunday, but Wednesday’s win lifts them a point above Arsenal and a point behind leaders Manchester United.
It was a gaffe from goalkeeper David James that presented Chelsea with a 32nd-minute lead.
He missed his kick while trying to deal with a bouncing ball as Deco headed on, leaving Drogba with an open goal.
Florent Malouda doubled the lead from Frank Lampard’s through-ball five minutes into the second-half, and scored his second 10 minutes later, snaffling the rebound after James had parried a Lampard shot.
Drogba then added his second from a diagonal pass from Dutch youngster Patrick van Aanholt.
Frank Lampard headed the fifth in injury-time.
Manchester City’s hopes of claiming fourth spot suffered a major blow as they lost 2-0 at home to Everton.
Tim Cahill headed in a Leighton Baines ball to give Everton the lead just after the half-hour. Mikel Arteta got the second five minutes from time after Cahill had dummied Jack Rodwell’s cross.
Aston Villa faltered, only managing a draw against Sunderland, who have now drawn six of their last nine games to edge to the brink of safety.
Fraizer Campbell scored his second in successive games to put Sunderland ahead from Kieran Richardson’s pass, but John Carew levelled from Ashley Young’s cross eight minutes later.
City trail fourth-placed Tottenham by two points, with Villa level with Liverpool, two points further back.
Sunderland, meanwhile, are now 11 points clear of the relegation zone and probably one win from guaranteeing safety.
Blackburn Rovers beat Birmingham City 2-1 in a game with little bearing at either end of the table.
David Dunn gave Blackburn the lead against his former club after five minutes, but James McFadden curled in a free-kick to level 10 minutes after the break.
Dunn, though, touched in an El-Hadji Diouf cross to restore Blackburn’s lead at the midpoint of the second-half.