The breakthrough came four minutes before the break and it went the way of Fulham as the unmarked Ayite tapped the ball in at the back post from a Sheyi Ojo cross.
On 51 minutes, the hosts wasted a great chance as Ayite played a telling ball into Ryan Sessegnon, who could only head wide.
They would seemingly come to rue that miss because, just two minutes later, Jarrod Bowen's close-range header on the rebound levelled matters at Craven Cottage.
Hull then came very close to edging into the lead in the 55th minute, but Ryan Fredericks did well to clear a goalbound effort off his own line.
However, Fulham regained their advantage just after the hour, Ayite miskicking with an overhead attempt before Stefan Johansen drilled home with a fine outside-of-the-foot finish.
The game finished on a flurry as both sides had several more chances to get further goals, but ultimately Slavisa Jokanovic's charges were able to hold on for all three points.