Both teams came into the game unbeaten in their first four matches in all competitions, but neither side was able to seize the initiative in a dull first 45 minutes.
The Addicks had the first genuine opportunity of the game a minute before the break when El-Hadji Ba flicked the ball into the path of Karlan Ahearne-Grant, but the substitute blazed over the bar from inside the penalty area.
However, just eight minutes after the restart Charlton broke the deadlock with the simplest of strikes, Simon Makienok heading home Johann Berg Gudmundsson's cross from the right for his first Addicks goal.
Gudmundsson could have doubled the lead minutes later when he was sent through one-on-one but his shot was denied by the face of Hull keeper Allan McGregor.
However, Charlton won it in the most dramatic fashion, when Makienok knocked the ball down for Gudmundsson to head past McGregor in the eighth minute of stoppage time.
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