The home side took the lead in the 13th minute when Evan Horwood's free-kick hit the underside of the crossbar and Andy Monkhouse reacted first to turn in a volley from eight yards for his fourth goal of the season.
Ryan Donaldson missed a tap-in for Pools in the 41st minute, shooting wide of an empty net after Antony Sweeney's long-range pile-driver had been pushed out by Charlton goalkeeper Rob Elliott.
But the visitors levelled in the 54th minute when Nathan Eccleston took Pawel Abbott's chipped pass, turned Steve Haslam and drilled past goalkeeper Scott Flinders.
The parity only lasted eight minutes. Another Horwood set-piece, this time a corner from the right side, was firmly headed in by Gary Liddle.
Powell's side went close to a leveller when Peter Hartley turned a shot from Ecclestone onto his own crossbar, but Pools were good value for an entertaining victory.