Early goals from Freddy Eastwood and Mitchell Cole were enough to see off our London rivals in an open and exciting encounter.
The Hammers got off to a flyer when Eastwood opened the scoring after just two minutes and Cole added a second 18 minutes later.
Tony Carr's team then had further chances to extend their lead and, although Charlton fought back to test keeper Glenn Jackson in the second half, the Hammers were always in control.
Said Carr afterwards: "We got off to a great start and dominated the first half. There were further chances to score and we could have been three or four up at half-time.
"Charlton came back into it in the second half and hit the post, but we defended well and fully deserved our victory in the end."
Team: Jackson, Lumsden (Morris 50), Tattum, Ward, Fletcher, Akinsete, Mehmet, Ritchie, Khan, Eastwood, Cole (Collington 80). Unused subs: San Lee, Pearson.