Charlton's best chance in a fairly tame first half came on the half-hour mark when Nicky Forster's flick-on was met by Deon Burton's ferocious volley from a tight angle but Shane Higgs made a reflex save to turn it past the post.
Caretaker managers Geoff Horsfield and Mark Grew achieved their first victory in charge of Vale, a 2-1 success against Burton Albion on Monday, to strengthen their grip on fourth position in League Two.