The Cod Army missed the chance of winning three league games in a row for the first time since March after second-half goals from Mason Burstow and Albie Morgan.
Morgan created talented teenager Burstow’s fifth goal of the season before wrapping up the points with his first goal for 14 months.
The disappointing defeat leaves Town just a point above the relegation zone and Lancashire rivals Morecambe after their five-goal thriller win against Wycombe Wanderers.
Stephen Crainey made a solitary change for the trip to the capital. Jay Matete replaced Portsmouth loanee Callum Johnson in the starting XI in south-east London.
The hosts were bidding for their first league win since mid-December and to maintain their proud record of never losing to Fleetwood at home.
Crainey’s visitors started brightly, with the returning Matete earning an early free-kick which Danny Andrew blazed over the bar.
But it was a sign of things to come in the first period as the Cod Army had the better chances.
Paddy Lane forced Craig MacGillivray into a save before Town captain Alex Cairns was called into action to keep out Sean Clare’s effort after he latched on to Dialling Jaiyesimi’s intricate pass.
The Lancashire side had huge shouts for a penalty waved away after Cian Hayes was bundled to the ground by Clare.
Defender Tom Clarke squandered a great chance when he nodded Andrew’s cross agonisingly over the bar.
Crainey’s charges continued to get into promising positions, without creating clear-cut opportunities to take the lead.
Just before the break, Clarke blocked Elliot Lee’s strike before Cairns produced a great save from his follow-up effort.
But it was a different story after the restart as the Addicks started the better of the sides.
Burstow was in the right place at the right time to head home Ryan Inniss’ knockdown from Morgan’s free-kick eight minutes after the restart.
Clarke was once again on hand to block a shot, this time from Chuks Aneke.
The visitors were let off as Morgan’s resulting corner flew straight in before being chalked off for a foul on Cairns on the hour mark.
Dan Batty’s desperate long-range strike barely troubled MacGillivray.
The best chance for an equaliser fell to Lane but he couldn’t poke substitute Shayden Morris’ teasing ball across the face of goal home as time started to run out.
Fleetwood huffed and puffed but failed to snatch a late point.
Ellis Harrison headed Andrew’s corner over the bar as any hopes of a share of the spoils slipped away.
Morgan dragged an effort wide in stoppage-time before putting the game to bed a minute later as he fired home with aplomb to secure a welcome win.
Charlton: MacGillivray, Clare, Inniss, Famewo, Jaiyesimi, Morgan,Dobson Gilbey 69), Blackett-Taylor (Purrington 86), Aneke, Burstow (Washington 81); Subs not used: Pearce, Leko, Watson, Henderson.
Fleetwood: Cairns, Johnston (Nsiala 81), Clarke, Jules, Andrew, Matete, Batty (Pilkington 75), Camps, Lane, Harrison, Hayes (Morris 61); Subs not used: Johnson, Biggins, Donaghy, Boyle.
Referee: Brett Huxtable
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