Jimmy Floyd Hasselbaink's 28th minute penalty decided a poor London derby and kept Chelsea in the hunt for the Premiership title.
Charlton for their part were terrible without even a shot on target for the whole 90 minutes.
Mark Fish was adjudged to have put his arm around Hasselbaink and referee Steve Bennett pointed to the spot, and the Dutchman stepped up to coolly send Addicks keeper Dean Kiely the wrong way before stroking the ball into the other corner.
The Blues were without established stars John Terry, Joe Cole, Carlo Cudicini, Claude Makelele, Damien Duff, Emmanuel Petit, Juan Sebastian Veron and Hernan Crespo - all out through a combination of injuries and suspensions.
"We should have scored more goals in the first half but had to fight in the second," said Chelsea head coach Claudio Ranieri.
"But we continued to press and had two or three chances." Those chances fell to Adrian Mutu who could have scored a hat-trick in two minutes.
First he shot wide from distance. He followed that up by rattling a post and then forced Kiely into a blinding save.
"We missed Makelele," confirmed Ranieri. "He gives us a certain tempo but Alexis Nicolas did very well.
Charlton manager Alan Curbishley admitted: "I was embarrassed and shocked with that first-half performance.
"We were lucky to get in at half time only one down, even if the penalty was a bit harsh.
"We had a couple of people missing and they were able to do whatever they wanted.
"We were a bit better in the second half, but we didn't really threaten.
"I want to draw the line under the Scott Parker affair - he's gone now and we have to get on with it.
"I can promise our supporters that they will see a much better performance on Wednesday when we play at home against Tottenham." Chelsea hit the woodwork twice - apart from Mutu's 84th minute effort, Jesper Gronkjaer's deep run and shot looped over Kiely but bounced unluckily off the crossbar after just four minutes.
Ranieri added that he didn't feel under pressure from the comments of new chief executive Peter Kenyon.
"I want to win, that is my aim. I want to win more than Mr Abramovich, Mr Kenyon and the fans," he said.