In what the Hoops' manager dubbed an "amazing" performance, Taarabt struck twice in the second half to secure the three points, though a late Mladen Petric goal led to a frantic last few minutes.
The midfielder's double ensured that his side finally move from the foot of the table as, though they still remain five points adrift of safety, the London side leapfrog Reading into 19th.
Redknapp previously managed Taarabt at Tottenham and was keen to both emphasise his player's talent and the tactical switch that enabled him to flourish against the Cottagers.
"[He has] fantastic ability, he was amazing. He is an amazing talent, we all know that and we have all seen it since I went to Tottenham, no-one ever doubted his ability or his talent," Redknapp told reporters.
"I decided I had to get him in a position where he wants to play. He has been playing off the left but today I played him in the hole, off the frontman and tried to get him between the lines - play little balls in those holes to him and every time he got the ball they were in trouble."
The former Spurs boss also spoke of his new club's future prospects, stressing how important today's win was and how it could ultimately kick-start their season.
"At least it keeps us in there, if we hadn't won today it would have been absolutely desperate. It is going to be tough, we are not going to kid ourselves but we have had one win but we are on a good run," he continued.
|KICK-STARTING THEIR SEASON|
|11/10||QPR are now 11/10 with Paddy Power to survive and escape relegation from the Premier League this season|
"We have had four games and taken six points. If you can take six points from every four games you will stay up - hopefully that can kick-start our season now and keep us going."
Meanwhile, Fulham boss Martin Jol was disappointed with his side's performance and lamented the fact that, despite fielding a similar team to the side that beat Newcastle 2-1, they could not produce the same standard of football.
"I'm very disappointed with our style of play - I can complain about the goals but especially first half we never looked to earn the right to use our quality, we looked a bit rigid," he told reporters.
"On Monday we had players in midfield, like they had Adel today, they need to travel and do something extra. We didn't do the simple things or play in the flow. I wanted to give 10 of the 11 players who played last week the chance to do it again but there were too many players not there."