Fleetwood’s quest to make it four wins in a row was thwarted by a late Lee Novak effort at Highbury.
Town made the perfect start with Chris Long pouncing on the loose ball and blasting the ball home from distance just four minutes in.
Charlton’s Josh Magennis nodded in Ricky Holmes’ cross in the 32nd minute but David Ball scored a peach of a goal as once again Town seized the loose ball in a dangerous position in Charlton’s half with Ball whipping the ball from the edge of the box into the top right corner just a minute before the break.
Town looked to have weathered a late Charlton storm but Chris Neal was just beaten to the ball by substitute Lee Novak who bundled the ball home with three minutes to go.
Fleetwood head coach made two changes to the side that beat Coventry 2-0 last weekend.
Kyle Dempsey and Conor McLaughlin, who returned unscathed from his international duty with Northern Ireland, came in for Eggert Jonsson who moved to the bench and Michael Duckworth who was missing due to illness.
It was a lightning quick start by Fleetwood as just seconds after unlikely attacker, captain Nathan Pond, fluffed his shot in the six-yard box, Long’s scoring streak continued. The on-loan Burnley man netted his third goal in as many league games in the fourth minute to fire Town on their way up the table.
He found himself in acres of space 25-yards out from goal and after spotting Rudd off his line he thundered the ball into the bottom corner.
It could have been an even better start for Town had Bobby Grant not wasted a free header in the 11th minute.
Dempsey, who was making his first league start for Town, whipped the ball from the right but the unmarked backpedalling Grant nodded wide at the back stick.
Fleetwood dominated proceedings but Charlton finally woke up in the 30th minute.
Town did not head their warnings as just seconds after the unmarked Nicky Ajose somehow failed to connect with Magennis’ knock down on the goal line Magennis popped up to show his strike partner how it is done.
Ricky Holmes whipped in a cross and Magennis was on hand to nod the ball down and past Neal in the 32nd minute.
Long carved out another chance for himself but his right-footed strike just fizzed wide of the left stick.
Charlton nearly took a shock lead as Ademola Lookman’s set-piece cannoned off Ball’s head towards goal, it took an age to drop as it looped up towards Neal’s goal but thankfully it fell over the bar.
And after Ajose lofted the ball way over the bar Ball showed him how it is done as he made it 2-1 in the 44th minute.
Cole was blocked by a royal blue shirt but the loose ball fell sweetly to Ball on the edge of the box who superbly curled the ball into the top right corner.
It was all that Fleetwood deserved at the break as apart from a five minute spell of Charlton pressure when the clock hit 30 Rosler’s men played the Addicks off the park.
Charlton came out fighting at the start of the second half but after carving out a chance Holmes smashed the ball wide of the left stick.
Charlton tried to exploit Town’s middle by switching more of their play to the wings but to virtually no avail as Town’s defence stood strong.
Cole lifted the ball over the bar as it became a game of attrition with the clock ticking on.
The game sprang back to life in the 75th minute as Ezri Konsa was booked for chopping Hunter down after the substitute had single-handedly launched a counter-attack from deep in his own half.
Konsa was booked for the bad foul and Grant smashed the subsequent set-piece over the bar.
Charlton should have drawn level moments later when Holmes’ shot was tipped away by Neal to Magennis at the back stick who hit the side netting.
And Novak’s angled chip from the left was just tipped over by Neal’s fingertips.
Referee Darren Handley waved away a penalty claim at both ends as time ebbed away with Novak claiming he was felled by Amari’i Bell in the box and the Cod Army claiming that a cross from Ball had struck Morgan Fox’s arm in the box.
But Novak popped up in the 87th minute to bundle home Foley’s pass from close range.
Fleetwood: Neal, McLaughlin, Eastham, Pond, Bell, Dempsey, Ryan (Jonsson, 46), B Grant (Woolford, 79), Ball, Cole (Hunter, 64), Long. Subs not used: Cairns, Bolger, Nirrenold, Jakubiak.
Charlton: Rudd, Lookman, Crofts, Magennis, Ajose (Novak, 60), Holmes (Botaka, 81), Konsa, Pearce, Ulvestad (Foley, 81), Solly, Fox. Subs not used: Bauer, Johnson, Phillips, Lennon.
Referee: Darren Handley (Bolton)