QPR finally won a league game at the 17th time of asking as they dispatched west London rivals Fulham 2-1 to move off the bottom of the pile.
The Rs have shown signs of improvement since Redknapp succeeded Mark Hughes at the helm, following up three successive draws with a first win here - thanks in no small part to Taarabt and they held on for three points despite substitute Mladen Petric's late strike.
A marauding Taarabt run through the middle ended in a strike that tested Mark Schwarzer as QPR continued to show a level of skill and spirit rarely seen this season.
Fulham were struggling to get a foothold on proceedings but were almost gifted an opener by goalkeeper Robert Green. Redknapp stuck with the England international despite the return of Julio Cesar from a groin injury - a move that almost backfired when he sent a miskick straight to Hugo Rodallega but the Fulham attacker could not make the most of it.
The opener came as, like so many times before, Taarabt made a burst forward but this time his strike took a lucky deflection of Brede Hangeland, wrong footing Schwarzer and trickling home.
The playmaker was booked for his celebrations but it could not stop QPR's momentum, with Cisse curling just wide in the 60th minute after Chris Baird was dispossessed.
Fulham were rarely threatening the hosts, who deservedly got their second when Taarabt burst through in the 68th minute. After picking up the ball just inside the Fulham half, the midfielder went past Hangeland and showed a few neat touches, before putting past Schwarzer with the outside of his right foot.
Petric ensured a nervy ending when his strike deflected in off Mackie's outstretched leg.