Both these clubs' main ambition for the season is to get promoted to the Premiership and this was reflected in the teams' selections with Charlton making five changes and Albion four.
After taking the lead inside two minutes, Charlton will be disappointed not to have gone through to the next round after creating, by far, the better chances in an open game which should have produced more goals.
A defensive mistake helped the Addicks score a soft goal through Zhi Zheng from close range after the visitors had failed to clear a corner from the right.
The home side should have increased their lead when Lloyd Sam fired over an empty net after former Charlton goalkeeper Dean Kiely had pushed out a shot from Izale McLeod.
Albion equalised with a well-taken goal, Ishmael Miller netting with a diving header from an excellent cross by Chris Brunt.
Albion made two substitutions at the break while Charlton brought on three new players after 76 minutes but it was Kiely in the visitors' goal that kept the home side at bay, making excellent saves from Luke Varney and McLeod with the Midlanders hanging on at the end.
After losing five matches at home this season, Charlton boss Alan Pardew switched to a 4-4-2 system which the team seemed a lot happier with, but Albion missed the fire-power of leading scorer Kevin Phillips who was rested for this match.
Charlton gave a debut to left-back Kelly Youga who has spent the last three months on loan at Scunthorpe United.