A last-minute own goal by Charlton goalkeeper Dillon Phillips saw Hull extend the Addicks' winless run to 10 games.
The first half of a 2-2 draw saw few clear-cut opportunities until Conor Gallagher's 34th-minute corner delivery to the back post was met by a firm downward header by Darren Pratley.
Jarrod Bowen then equalised with his 15th Sky Bet Championship strike of the campaign before Naby Sarr put the hosts in front soon after.
Lee Bowyer's men looked set to hang on for a precious three points, but were undone as teenager Keane Lewis-Potter's header hit a post and squirmed over the line after hitting Phillips' back.
Charlton came into the game low on confidence having picked up just two points from their last 27, but the hosts enjoyed the first real chance of the contest after 12 minutes. Gallagher's cutback just across the box was knocked away, but only as far as Albie Morgan, whose rasping drive was blocked.
Then came the Charlton breakthrough. Centre-back Tom Lockyer collected the ball inside the Hull half and slipped in Jonathan Leko, whose ball across the box seemed to strike the hand of the sliding Jordy De Wijs before going behind.
Despite feverish home protests, they did not have to wait long for their mood to improve as Gallagher's resulting delivery was nodded home by Pratley for his first goal of the season, despite the attempts of several Hull players to clear it away.
Bowyer's men were hitting their stride, and a whipped cross by Adam Matthews narrowly missed a couple of red shirts, when any contact on the ball would have made it 2-0.
After another Morgan effort went close, Charlton will have gone into the break ruing the fact they were not further ahead.
Their wastefulness was quickly punished when the teams returned. After Bowen had seen a shot blocked just moments earlier, the striker tapped in after an inviting cross from Kamil Grosicki.
The Charlton response was almost immediate. The exciting Leko jinked his way down the right wing and towards the Hull box on the hour mark. His swept ball across evaded Macauley Bonne, but Sarr was on hand to score his second of the campaign.
The visitors still posed a significant goal threat, with Lockyer's impeccable sliding tackle nipping the ball off Grosicki's toes with the Pole poised to cut inside and shoot.
Hull penalty protests were then waved away after Jackson Irvine looked to have caught a stray boot from Pratley before Bowen's swivelled volley was tipped away smartly by Phillips.
As the seconds ticked down, it looked as if the south-east Londoners would hang on for a priceless three points, but minutes after Phillips had been at his agile best to paw another effort away, he became the victim of the cruellest ending, as substitute Lewis-Potter's header trickled out of the 24-year-old's reach.
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