Hull boss Sergej Jakirovic reverted to a back three, matching the Charlton system, and the change seemed to unsettle the home side who could have been two down inside the opening four minutes.
Charlton’s Tyreece Campbell met a long cross-field pass and his left-foot volley was well saved by Croatian keeper Ivor Pandur. Campbell then side-footed over the bar a minute later.
The hosts’ best early chance saw defender Ryan Giles going close, with his shot deflected wide of Thomas Kaminski’s goal.
The Belgian keeper then saved twice from Nigeria defender Semi Ajayi, foiling one effort down low before making another good close-range stop.
Hull made the perfect start to the second half, scoring in the opening minute through Gelhardt. The 23-year-old picked up the ball just inside the box, taking two touches before a clinical finish into the corner of Kaminski’s net.
Space opened up for the Tigers as the visitors pressed for an equaliser. Regan Slater saw his shot blocked, before substitute Amir Hadziahmetovic’s effort from outside the box was also blocked.
Charlton boss Nathan Jones brought on Charlie Kelman and Berry with 20 minutes to play, making it four up front.
And it was Berry who rescued a point for the Addicks, equalising in the 91st minute from close range from a corner.
There was another negative for the hosts as midweek goal hero Liam Millar limped off just 13 minutes after coming on as a substitute. His start against Leicester City on Tuesday had been his first appearance for just under a year.