First away win since October for Martin Jol's side as the home fans call for Mark Hughes' head following fourth defeat in five games for the promoted side
Pogrebnyak opened the scoring early on as Moussa Dembele found him clear through on goal with a backheel, and the Russian rounded Paddy Kenny to score in an empty net.
The big team news of the day came from the QPR dressing room, with Mark Hughes naming Bobby Zamora in the starting lineup against his former club, and midfielder Samba Diakite making his debut.
Martin Jol also named his January striking acquisition in the starting XI, as Pavel Pogrebnyak combined with Andrew Johnson up front.
Both teams started brightly, cheered on by some extremely loud support from their fans, and Fulham had the ball in the back of the net with not even five minutes on the clock.
Andrew Johnson headed the ball in off the bar from John Arne Riise's cross, but it was ruled out for offside.
It didn't take long for Fulham to take the lead, however. Moussa Dembele created the goal with a fine backheel to send Pogrebnyak clear through on goal. The Russian striker stayed calm, rounded Paddy Kenny and placed the ball into the back of the net.
The visitors were looking like scoring every time they went forward, with Clint Dempsey dragging a shot just wide of the far post soon after the goal.
But QPR soon picked itself up and started playing. Mark Schwarzer was on hand to prevent the home side going level with an incredible save on Zamora. The goalkeeper initially spilled an effort by Shaun Wright-Phillips, but spread himself really well to block Zamora's effort on the rebound.
The game really turned in Fulham's favor just after the half-hour mark when Diakite picked up his second yellow card of the match. The midfielder had picked up a yellow for repeated offenses and got his marching orders for a bad tackle on Bryan Ruiz in the center circle.
Ruiz didn't help matters with some rolling around following the tackle, but Diakite gave referee Phil Dowd no choice but to send him off, becoming the third player in QPR's last four home league games to be sent off in the first half, after Joey Barton against Norwich and Djibril Cisse against Wolves.
Following the red card, Fulham began to dominate possession once again, with Danny Murphy keeping the ball moving well and Dembele enjoying more time on the ball in a deeper role than usual for the visitors.
Fulham went in at halftime on top, and leaving Mark Hughes with some serious thinking to do about his side for the second half.
The second half didn't really get going for a while. Fulham was content to sit back and defend its lead, waiting to hit back on the counterattack.
It was a dangerous tactic, with QPR going close in the 69th minute as Mackie powered through the defense before seeing his shot flash across the face of goal.
The home side didn't really come close again until the 82nd minute when Wright-Phillips missed a fantastic chance as he was through on goal, but his shot went wide, and it looked as if Schwarzer got a hand to it.
Fulham almost doubled the lead in the closing stages as Dickson Etuhu came on from the bench, drove through the defense but crashed his effort wide.
However, it was enough for Fulham, which held on for its first away win since late October.