A stunning 30-yard free-kick from Daniel Fox secured victory for Coventry over bottom-of-the-table Charlton.
Robbie Simpson opened the scoring for the home side when he finished Fox's left-wing cross beyond Nicky Weaver for his first league goal of the season.
Deon Burton levelled matters from the penalty spot in the 49th minute after Ben Turner had felled Izale McLeod.
But Coventry took all three points when Mark Hudson conceded a free-kick and Fox stepped up with a curling effort.
Charlton caretaker boss Phil Parkinson:
"All I'll say is that (chairman) Richard Murray and the board have worked tooth and nail to get this club in the position it is in. We have the responsibility as a group to keep it there, but it's fairly obvious change needs to happen.
"The board have been incredibly supportive, they know I'm doing all I can to turn it around and they haven't said anything about the short term or the long term.
"If it happens I'll walk away with my head held high. But I'll fight on for as long as I'm in charge and I'll continue to work hard."
Coventry manager Chris Coleman:
"We felt if we could keep them quiet, get on top and make them make mistakes then the fans would get on top of them. We played on the counter-attack and it worked.
"But it's hard walking off at the end. It's not a lack of hard work, things just aren't coming off for them."
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