Wolves have climbed off the bottom of the table thanks to a Jose Bosingwa own goal which allowed them to record a 1-0 win at the Molineux.
The three points allowed the Wolverhampton club to move up to 17th with teams below them Aston Villa and West Ham United losing and Wigan Athletic being held to a draw.
Chelsea stayed fifth but are only two points clear of sixth-placed Sunderland who won at Villa.
Wolverhampton Wanderers: 1 (Jose Bosingwa (og) 5') Chelsea: 0
Venue: Molineux Stadium, Wolverhampton Crowd:26,432 Referee: Mark Halsey Yellow cards:WW - nil CHE - Branislav Ivanovic 45'
GOAL Things started dismally for the reigning champions when Jose Bosingwa turned in a corner under pressure from Steven Fletcher. Wolves would not have minded how they got the opener, as long as it went in.
Noteworthy action did not come again until just before the half-hour mark when Kevin Doyle's shot was saved by Petr Cech before Wayne Hennessey was called on down the other end to keep out Salomon Kalou's attempt from a Florent Malouda cross.
Chelsea were well on top in the second term with Malouda and Ashley Cole testing Hennessey before Drogba hit the post in the 66th minute.
Wolves midfielder Stephen Hunt struck the crossbar in the 71st minute which was the only real joy the home side had in the attacking third as the Blues tried desperately for a leveler but could not find one as Mick McCarthy's men climbed off the bottom of the Premier League table.