The only goal of the match was scored by Ryan Sessegnon in the 43rd minute, while in the 66th minute, Timothy Castagne found the back of the net again, but the goal was disallowed due to an earlier foul on goalkeeper Villa.
Fulham sits tenth in the table with 48 points, while sixth-placed Brighton has just two points more and a game in hand over the London side.
On the other hand, Villa is fourth in the table with 58 points, but is fairly secure in its qualification for next season's Champions League.
In the next round, Fulham will visit Arsenal, while Aston Villa will host Tottenham at home.
Result and scorer: Fulham - Aston Villa 1:0 (Sessegnon 43')