After a 2-1 victory at Southampton last weekend, Rangers impressively came from behind against Sunderland at Loftus Road on Saturday afternoon.
Steven Fletcher gave Martin O'Neill's side a 20th-minute lead against the run of play, but Loic Remy levelled things up 10 minutes later.
It had looked like the spoils would be shared as both sides struggled in the second half, only for exquisite half-volleys from Andros Townsend and Jermaine Jenas to earn QPR a 3-1 victory.
The west Londoners remain bottom of the standings and four points adrift of safety despite the win, although Redknapp believes they can still get out of trouble.
"It's good, but we are still in need of a fantastic run," the Rangers boss said. "We have given ourselves a chance.
"We have closed the gap and any team on 30 points is not safe. You can go eight, nine or 10 games without winning quite easily.
"Anyone can have a bad run now and if we continue to pick up points we may have a chance. It won't be easy but we have given ourselves a chance.
"I saw Wigan today [Saturday] and thought they were fantastic. They are a good side.
"Aston Villa are not a bad side. There are teams that are capable of putting together a few results.
"We can put together a decent run, too. I think there are a few teams above us who could get sucked in."
Redknapp will be hoping to have Adel Taarabt, Julio Cesar and Armand Traore available for the relegation run-in after the trio missed Saturday's match through injury.
Bobby Zamora could have also missed out but fought through the pain barrier, managing 73 minutes before hip and ankle knocks got the better of him.
"Zamora wasn't really fit, he has done a miracle with his ankle ligaments," Redknapp said.
"He is playing with an injury today [Saturday] that other players wouldn't have put themselves up to play.
"There are players not playing today [Saturday] with injuries that aren't as bad as Bobby's, that's for sure. He has a go and has done that today [Saturday].
"You can only play what you've got, and this is the first time I've had Bobby and Remy. I liked the look of them.
"Bobby can hold the ball up and Remy has pace and can score goals. I thought they would be an ideal combination.
"They will be important. If Remy can continue to score and Bobby gives us a focal point, we can play it up to him.
"Bobby played 60 per cent fit today [Saturday]. The physio said a week ago he would be out for six weeks.
"He did his ankle but he has had injections to play, he was so desperate to get out there. The effort he has put in to play was fantastic."
For Sunderland, Saturday afternoon was a case of what could have been as two wonder strikes separated the sides.
The Black Cats have now lost four of their last five league matches and are in danger of being sucked into a relegation battle, which Redknapp believes requires 37 points to avoid.
"We have 30 on the board," Sunderland boss O'Neill said. "He was speaking from a position of having 20, so you have to try and win those games.
"His team needed 17 from the last 10. That is European form. We need to start winning, really. I think next week is a big, big game for us.
"We have difficult fixtures coming up, including Norwich. We have our work cut out. We have known that since the start of the season.
"It has been tough going throughout the season and we have to fight through these last nine games.
"I was asked about being close to 10th and close to being relegated yesterday [Friday]. It will be like that until the end of the season."