Despite an impressive comeback, the visitors were unable to make amends for a nightmarish first half in a truly exhilarating west London derby at Craven Cottage
A first-half to forget for the visitors started after only eight minutes when Berbatov calmly converted from the penalty spot, and the Bulgarian doubled their lead 14 minutes later after a defensive mishap from Christopher Samba.
Hill deflected the ball into the back of the QPR net after 40 minutes to put the home side 3-0 up, but Adel Taarabt pulled one back for the visitors when he fired in on the stroke of half-time.
QPR's performance transformed from a nightmare into a dream after the restart, with Loic Remy pulling the deficit back to only one with an early goal, but Fulham, despite going down to ten-men late in the second half, were able to hold on to deny the Hoops a truly historic comeback.
The home side named an unchanged starting 11 from the one that beat Tottenham 1-0 at White Hart Lane, with that game's only goalscorer Berbatov leading the line.
Meanwhile, Harry Redknapp made two changes to the side that lost 3-2 to Aston Villa, replacing Park Ji-Sung and Fabio with Armand Traore and Adel Taarabt.
An experienced and regimented Fulham side started arguably the stronger of the two teams, carving out good early chances whilst keeping the QPR attacking force at bay.
Their pressure paid off when Samba was forced into scything down Ashkan Dejagah just inside the QPR penalty area after eight minutes, leaving referee Lee Probert with little choice but to point to the spot.
Berbatov stepped up and coolly put the ball away past Julio Cesar to give the home side an important early lead.
Fulham's dominance continued in full force right from the restart as a lacklustre QPR side looked nervous at the back, and their vulnerability culminated in a terrible mistake from Samba after 22 minutes that gifted Berbatov with his second goal of the game.
The big Congolese defender took too long on the ball and lost possession inside his own penalty area, allowing the Bulgarian to break free in front of goal and calmly side-foot the ball into the bottom corner of the net.
Their lead was then extended to three goals with five minutes of the first half left to play when, unable to deal with a cross from John Arne Riise, Hill put the ball into the back of his own net with his shoulder.
Already 3-0 down after only 41 minutes, QPR looked dead and buried but Taarabt was on hand to pull a goal back at the end of the first half with a wonderful solo effort that ended with the Moroccan firing in an unstoppable low shot past an outstretched Mark Schwarzer.
Spurred on by Taarabt's equaliser, QPR started the second half in top gear and were rewarded with a penalty after 48 minutes when Giorgios Karagounis fouled Taarabt on the edge of the penalty area.
The spot-kick responsibility was given to Remy but Schwarzer was able to palm the Frenchman's tame effort into the path of Damien Duff, who cleared the ball from danger.
The visitors continued fighting at full force, however, and Remy was able to atone for his miss when he put his side back into the game just three minutes later with a rocket of a shot that bounced off the crossbar and over the line.
In stark contrast to the first half, QPR remained on the front foot for the remainder of the second half, and things went from bad to worse for Fulham when Steve Sidwell was shown a straight red card for a rash challenge on Traore with little over 10 minutes left to play.
Despite a plethora of chances, the visitors were unable to capitalise on the one-man advantage and a visibly nervy home side were just about able to hold on for the remaining moments to secure a hard-fought win and deny QPR a memorable and important comeback.