Despite a virtuoso performance from 16-year old Charlton midfielder Jonjo Shelvey, the Addicks were unable to break their winless hoodoo and have now gone 17 matches without a victory.
Shelvey became the youngest player in Charlton's history to score, when he found the back of the net after 19 minutes with a sweet strike and his side should have gone on to win against a Norwich team who failed to have a shot on goal in the opening 45 minutes.
Charlton were denied that elusive second goal when goalkeeper David Marshall tipped over Deon Burton's header and then made another fine save from the Charlton striker.
The introduction of Wes Hoolahan for Norwich in the second half gave them the initiative and the little midfielder shot wide from the visitors' best chance.
But another of their substitutes Arturo Lupoli equalised in the 70th minute to set-up the replay by turning well before firing into the net.
Charlton gave a much better performance despite the fact that they were without two or three of their regular players, while Norwich ended a recent depressing run of six defeats in their last eight games.
The East Anglian side have been knocked out of the third round of the competition in nine of the last 11 seasons, but they will fancy their chances of progressing when the teams meet again.