The victory has moved Unai Emery’s side back into fourth position in the Premier League table, with Tottenham Hotspur losing 2-1 at home to Wolverhampton Wanderers on the same afternoon.
Villa had the ball in the back of the Fulham net inside the first two minutes at Craven Cottage through Watkins, who finished after a brilliant pass from Youri Tielemans, but the offside flag disallowed the goal.
Fulham’s first half-chance came from Rodrigo Muniz, who scuffed one wide from distance, with both teams struggling to find their rhythm in the early stages of the clash in the English capital.
Jacob Ramsey was dangerous for Villa, though, sending one wide in the 12th minute after a mazy run, before Muniz missed the target down the other end after being released by Andreas Pereira.
Fulham had a shout for a penalty in the period that followed, with Bobby De Cordova-Reid nudged in the back by Pau Torres, but the referee was happy with the challenge and VAR agreed.
The home side then had a goal chalked off, with Tim Ream’s effort disallowed for offside after a free kick had been flicked into a dangerous area by Joao Palhinha.
Less than one minute later, Villa had the lead, with Watkins finding the back of the net with a clever finish after Ramsey had made the most of some poor defending from Fulham.
Leon Bailey came close to a second for Villa in the period that followed, but effort from distance rattled against the crossbar in a huge let-off for the home side.
Villa thought that they had scored a second late in the first period through Alex Moreno, only for his header to be disallowed following an offside check, before Muniz dropped a header just wide of the far post in the final stages of what was an entertaining first 45 minutes.
There were actually two more chances for the visitors before the interval, but Tielemans saw his effort kept out by Bernd Leno before Bailey’s effort was then deflected over the crossbar.
Villa did have a second in the 56th minute, though, with Watkins collecting a pass from Tielemans before finding the back of the net with an excellent finish.
Fulham were back in the match in the 63rd minute, with Muniz tapping in at the near post following an excellent cross from Antonee Robinson.
Harry Wilson almost levelled with a clever effort in the period that followed, but his side-foot volley from a Pereira free kick just missed the target, before Adama Traore was denied by Villa goalkeeper Emiliano Martinez in stoppage time, as Emery’s side picked up a huge three points in their battle to qualify for next season’s Champions League.
