The Cottagers, who were beaten by their West London neighbours earlier in the season, got off to the perfect start and went three up.
Bulgarian Berbatov scored in his fourth consecutive game as he calmly rolled home an early penalty before adding a second soon after.
An own goal by Clint Hill gave the Cottagers a seemingly unassailable lead, but Adel Taarabt's strike late in the first half gave QPR a glimmer of hope.
Loic Remy then saw his penalty saved by Mark Schwarzer before making amends just minutes later but Harry Redknapp's side could not find the equaliser and now remain seven points from safety with seven games of the season remaining.
Last season QPR suffered an embarrassing 6-0 defeat at Craven Cottage and it looked like there could be a similar scoreline after a dominant first-half display by the hosts.
Marquee January signing Christopher Samba gifted the Cottagers their first two goals, bringing down Ashkan Dejagah to allow Berbatov to net an eighth-minute penalty. Things got worse soon after when Samba lost possession of the ball on the edge of his own box, allowing Berbatov to coolly slot home past Julio Cesar.
Chants of "going down" echoed around Craven Cottage when Hill put a John Arne Riise cross into his goal, but QPR rallied and launched the unlikeliest of comebacks.
Taarabt, who stormed out at half-time of last season's Craven Cottage encounter, reduced the deficit on the stroke of half-time firing low past Schwarzer.
Six minutes into the second half, referee Lee Probert pointed to the spot after Giorgos Karagounis was fooled by the quick feet of Taarabt, but Remy's penalty was saved to his left by Schwarzer.
The France international, though, soon made amends, losing marker Philippe Senderos and continuing forward before thrashing home off the underside of the bar.
The veteran Australian had to be at his best for the rest of the match and, despite Steve Sidwell's late sending off, Fulham held on, condemning QPR to a potentially season-defining defeat and leaving their Premier League status in serious danger.