The Bulgarian forward was in fine form as he netted a wonderful strike from inside the box before converting a penalty, with Steve Sidwell adding a late third for the hosts
The Bulgarian striker netted twice in the first half, with the first coming after half an hour with a wonderful effort into the top corner, and another coming from the spot on the stroke of halftime, with Baggies attacker Peter Odemwingie seeing red for a stupid kick five minutes before.
Sidwell wrapped up a deserved victory moments from the end, crashing a half-volley into an unguarded net.
Fulham started brightly, and almost took the lead when Berbatov tried to get on the end of Sascha Riether's cross, but Jonas Olsson was there to prevent him getting a touch.
Fulham was pressing more and more as the first half wore on, and eventually found an opener just after the half-hour mark. Alex Kacaniklic had been finding lots of opportunities to run at Jones, and this time he found Berbatov, who had time to take a touch and curl home a great effort into the top corner.
A little over five minutes later, Fulham's task was made a whole lot easier as Odemwingie inexplicably kicked out at Riether after losing the ball. It was a terrible decision from the striker, right in front of the home dugout, and he was swiftly shown the red card by referee Roger East.
And as the first half entered stoppage time, it looked to be all over as Kacaniklic rampaged down the left again, being brought down by Jones in the area for a clear penalty. Berbatov stepped up and made it look simple, sending Ben Foster the wrong way to double the lead at halftime.
The second half started with a double swap for the visitors as Marc-Antoine Fortune and Shane Long were replaced by Romelu Lukaku and Chris Brunt, and for a while the game lacked any real sort of tempo.
However, as the half progressed, Fulham got more and more dominant. Lukaku forced a decent stop from Schwarzer after a deflection, but it was Foster who really began to impress in goal.
The former Manchester United man made three fantastic stops in the space of a couple of minutes, with the third an outstanding reflex move to push the ball over the bar from Damien Duff's wickedly deflected shot.
The home side's dominance was pretty clear, with attack after attack being launched on the Baggies' goal, and only Ben Foster really impressing for the visitors.
Fulham's dominance was realized in the dying moments, when Sidwell crashed in a rebound after Rodallega's header hit the bar following good work from substitute Pajtim Kasami.