Centre-back Lowe saw red for a nasty foul on Scott Wagstaff with six minutes left as a spirited display by the non-league side ended in misery.
Matthew Taylor headed Charlton in front in the 40th minute and a late flurry made it emphatic, with Johnnie Jackson getting the second with 10 minutes to go before further strikes from Danny Hollands and Bradley Pritchard.
Charlton will now face Carlisle United in the second round.
Morecambe saw an 89th-minute header from Gary McDonald ruled out for offside as Sheffield Wednesday progressed with a 2-1 win on the Lancashire coast.
The Shrimps thought they had erased a 2-0 deficit when McDonald nodded home the rebound from Phil Jevons' saved shot, but an assistant's flag denied them.
Chris Lines had fired Wednesday in front in the 18th minute and Chris O'Grady headed in a second seven minutes into the second half, but a controversial penalty - given for a handball by Lines - allowed Laurence Wilson to get the hosts back in it just after the hour mark.
Wednesday will now await the replay between Maidenhead and Aldershot, who drew 1-1 on Saturday, to see who they play in the second round.