The Londoners have won only once at home in 7 matches this season - in August - and they were always second best against a City side that dominated the game throughout.
After a great start to the season which saw them win 5 successive Premiership away matches, Charlton's form has disintegrated because of their terrible defending and they have failed to keep a clean sheet in 13 matches, the root cause of their present problems.
Although they coasted home in the end, City almost made it difficult for themselves with a couple of their own defensive aberrations but Stuart Pearce's side were good value for only their second Premiership victory in 13 matches against London clubs in the capital.
It was another frustrating and worrying day for Charlton boss Alan Curbishley, who certainly did not enjoy his 700th match in charge.
The Addicks boss recently expressed disappointment at his team's performances and has admitted he has seen his first grey hairs recently. He will certainly have got some more after this Kamikaze showing by his team who are completely devoid of confidence.
But take nothing away from City, who had themselves been in a mini-slump, especially on their travels.
Manager Stuart Pearce made 5 changes to the side that lost against Liverpool, bringing back the experienced Claudio Reyna, Ben Thatcher, Trevor Sinclair and Sun Jihai as well as David Sommeil, who played with a face mask and took over from injured former Charlton star Danny Mills.
City dominated the first 20 minutes and had 2 or 3 chances to go in front, the best falling to Darius Vassell who beat the offside trap to go one-on-one with Charlton goalkeeper Dean Kiely. However, the Republic of Ireland international, playing his first Premiership match of the season, produced a brave save.
It was no surprise when the visitors took the lead on 25 minutes, Andy Cole scoring his 182nd Premiership goal and his 6 of the season after good work by Vassell.
Charlton had a great opportunity to equalise but Darren Ambrose fired wildly over the bar with only David James to beat.
The home side did score after 35 minutes, but their joy lasted only 54 seconds.
Richard Dunne edged forward and missed a header, leaving Darren Bent free to give David James no chance with his 10th of the season and first in 6 games.
But City soon regained their lead - Cole played Sinclair in and Kiely might have done better with the low angled drive which eluded him.
Charlton brought on Jerome Thomas after the break as they looked for more width by reverting to a 4-4-2 system. But they found themselves further adrift on 69 minutes when Vassell was fouled in the area by Hermann Hreidarsson after a great flowing move by City.
Up stepped Joey Barton, who had already gone close with two 20-yard drives, and although Kiely saved his weak spot-kick, the midfielder tucked home the rebound in front of England boss Sven-Goran Eriksson.
Charlton battled back into the game with substitute Jay Bothroyd crashing home a 20-yard free-kick and then Thomas saw his shot well saved by James.
However, the visitors completed the rout with two late goals as a result of more dreadful defending by the home side.
Vassell made it 4-2 after being played in by the brilliant Cole, and the former Manchester United, Newcastle and Fulham striker then put the icing on a fine personal and team performance with his side's 5th goal after he intercepted an awful back header from Chris Perry intended for Kiely.