After Yasin Ayari produced a moment of magic to put the visitors in front in the first half, the Cottagers equalised through substitute Samuel Chukwueze before Wilson produced the winning strike in the 92nd minute.
Fulham were in the ascendancy when Ayari picked up possession on the left and cut inside before unleashing a venomous strike from the edge of the box past the diving Bernd Leno in the 28th minute.
The Seagulls almost doubled their lead two minutes later when Leno kept out Kaoru Mitoma’s initial effort before Ferdi Kadioglu’s header on the rebound was cleared off the line by Timothy Castagne.
The game opened up in the early stages of the second half and Fulham drew level through Chukwueze, who latched on to a long ball from Joachim Andersen and slotted past goalkeeper Bart Verbruggen to restore parity.
Brighton thought they had regained the lead a couple of minutes later only for Danny Welbeck’s effort to be ruled out by the video assistant referee for offside before the striker also had a header tipped over the bar.
However, it was the hosts who found the decisive goal in the stoppage time as Wilson beat Verbruggen from 25 yards with a free-kick awarded for a foul by Charalampos Kostoulas on Josh King.
Fulham climb to seventh in the Premier League table with 34 points while Brighton are four points behind in 12th.
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