Jermaine Jenas' early tap-in was cancelled out by Simon Dawkins's equaliser but Rangers sealed a 2-1 win in the 63rd minute when the ball ended up in the back of the net as Clint Hill, Jenas and visiting defender Jake Buxton challenged for Faurlin's right-wing free-kick at the far post.
However, the home side's afternoon ended on a sour note after fans' favourite Faurlin, who suffered cruciate damage the season before last, was carried off with 15 minutes remaining.
Redknapp now plans to enter the loan market after losing another key player.
He said: "It was a good game, it's just a shame about Ale. He's done his knee and it doesn't look very good.
"I wouldn't want to make a judgement but it looks like a bad injury. He'll go and have a scan.
"The kid's got back into the team and played well and now that's happened to him today.
"I don't know how he did it to be honest, but it's such a shame for the lad. He gives us a good balance in midfield."
"I've been pleased with our performances. It's a tight division but we'll be up there at the end of the season.
"We have picked up a few injuries though and might try to get a loan or two in if we can.
"Niko Kranjcar pulled his hamstring, Tom Carroll recently picked up an injury and Gary O'Neil too, so we are getting injuries."
QPR went ahead on 11 minutes when Jenas tapped into an empty net after Charlie Austin's close-range effort had been parried by keeper Lee Grant.
Dawkins volleyed home after Jamie Ward's free-kick had been headed down by Buxton, but lead was restored when Hill, Jenas and Buxton tangled and the ball went in after Faurlin's free-kick.
It meant an unhappy return to Loftus Road for Steve McClaren, who recently left a coaching role at Rangers to take over as Derby manager.
"My team can be proud of their performance," McClaren said after the Rams' first defeat since his appointment.
"I know from working here with QPR's players that they're the best team in the league and will have no problems going up with the squad they've got.
"We stopped them playing and did everything well without the ball in the first half, but we could have been better with the ball.
"We caused them problems in the second half, swamped them and five minutes into extra time were still going strong and were unlucky not to get something.
"We've got a lot of things to work on but if we keep doing what we did today, with the same endeavour, we'll win more games than we lose.
"The results will take care of themselves if we work hard and play football. I couldn't wish for a better group to work with.
"This is all about the long term. It didn't work out for us today but most of the time it will."