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City thought they had levelled midway through the half when Davis had the ball in the back of Stephen Henderson's net, only to be penalised for offside.
Vetokele, arguably Charlton's greatest threat in the first half, then set up Johnnie Jackson, only for the captain to be kept out by Randolph.
Andre Bikey squandered a good chance to increase the Addicks' advantage on the stroke of half time when he headed another Bulot cross over the bar.
They were punished seven minutes into the second period when Davis latched onto Stephen Gleeson's cross before beating Henderson with a shot from the edge of the area.
City went in search of a winner and David Cotterill may feel that he should have done better on 77 minutes when he collected Clayton Donaldson's headed pass, but put his shot well over the Charlton crossbar.