After a 2-1 victory at Southampton last weekend, Rangers impressively came from behind against Sunderland at Loftus Road.
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 [at Everton] 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."