Alex Iwobi struck the winner in the 33rd minute to lift the home side off the foot of the Premier League table and out of the bottom three, though goalkeeper Konstantinos Tzolakis will wonder how he ever let the shot spill through him.
Fulham had dropped eight points from winning positions this season, including five when they had led inside the final two minutes, and their wastefulness after going in front was alarming, if not ultimately costly.
Gonzalo Garcia in particular spurned a golden opportunity when he headed against the crossbar with the six-yard box to himself. It was the kind of chance the former Real Madrid striker was brought in to bury, and Fulham may yet find their position remains perilous if they continue to give up chances like this.
Hull were a pale impression of the team that had begun the season with such attacking ambition, and the passiveness with which they approached a game against the side propping up the league will have been of concern for Sergej Jakirovic.
Fulham dominated from the start and went close when Iwobi’s shot was deflected on to the roof of the net in the third minute.
The hosts were playing like a team desperate for a win, with Oscar Bobb and Timothy Castagne in particular menacing Hull down their left.
The breakthrough came just after the half hour. Brooke Norton-Cuffy’s clearance was poor and from there Hull never recovered. Sander Berge took possession and knocked it back to the edge of the box for Iwobi, whose driven finish squirmed through the body of Tzolakis. The goalkeeper could point to a slight deflection, but it was a poor error.
In the second half, Tzolakis partially redeemed himself with a good save with his feet to deny Josh King, after Semi Ajayi had played his team into a mess with an awful pass out of defence.
Fulham were beginning to show what they were capable of. King’s touch on the hour to spin away from Ajayi was a delight. The 19-year-old then drove forward and crossed for Garcia to head into the path of Iwobi, and only a magnificent save from Tzolakis denied the Cottagers what would have surely been one of the goals of the season.
Iwobi came close again with a curling effort that dropped just wide of the near post.
Hull were clinging on, but all the while the spectre of dropped points hung over Fulham as long as the second goal eluded them.
Nervousness around the ground intensified after Garcia planted a free header against the crossbar from six yards.
But they held on despite Sessegnon, on as a late substitute, being dismissed with virtually the last action, though there was clearly no violent intent behind his challenge on Vaz.