Goals from Darren Ambrose and Andy Reid helped guide last season's beaten Carling Cup quarter-finalists Charlton safely into the second round.
Ambrose capped a fine team move to put the Championship title favourites ahead seven minutes after half-time.
Charlton extended their lead 10 minutes later when Republic of Ireland winger Reid converted a twice-taken penalty.
Swindon best chance came early on when Lee Peacock's shot was blocked on the line by Yassim Moutaoukil.
Swindon: Brezovan, Jack Smith, Tozer, Ifil, Aljofree,
Roberts (Pook 59), Adams, Easton, Comminges (Zaaboub 59),
Peacock, Sturrock (Arrieta 75).
Subs Not Used: Phil Smith, Vincent.
Charlton: Weaver, Moutaouakil, Powell, Bougherra, Semedo, Sam, Reid (Sinclair 79), Ambrose, Fortune, Bent (Iwelumo 78),
McLeod (Dickson 82).
Subs Not Used: Randolph, McCarthy.
Goals: Ambrose 52, Reid 63 pen.
Ref: K Woolmer (Northamptonshire).