The former Tottenham playmaker opened the scoring with a long-range effort which deflected off Brede Hangeland and past Fulham goalkeeper Mark Schwarzer in the 52nd minute.
Taarabt then extended QPR’s lead eight minutes later, with the Morroccan dribbling past a number of defenders before curling a shot into the top corner of Fulham’s net.
Mladen Petric netted a late consolation but the Hoops clung on to move to within five points of safety, with Redknapp heaping praise on Taarabt.
“Taarabt is an amazing talent, I sold him at Tottenham but I never wanted to do that,” Redknapp told BBC Sport.
“He is a fantastic footballer, he has the ability to be up there with the best. He has all the ability in the world.
“I thought it was one of the all-round great individual performances. Everything he did was top class. He has all the talent to be whatever he wants to be.”
Redknapp also praised his side for an impressive defensive display despite a nervy couple of minutes after Petric’s 88th-minute strike.
“I cannot ask any more than they gave today,” Redknapp added.
“[Fulham boss] Martin Jol has done a great job with them, but I thought we were much the better team. We defended for our lives and got what we deserved.
“That last four minutes when you see a 2-0 lead go to 2-1, you keep looking at the referee and there are not many better feelings in life when he blows that whistle.”
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