Keith Millen's first match back in caretaker charge of the visitors saw a well-fought draw which leaves the visitors just one point away from safety while QPR move up to 15thQPR and managerless Crystal Palace battled their way to a 0-0 draw at Loftus Road.
Keith Millen took caretaker charge of the side after Neil Warnock's dismissal, and his side had the better of the chances in the first half with Jason Puncheon's well-struck drive from 20 yards only denied by the left-hand post.
The draw moves Palace to one point away from safety, while Harry Redknapp's side climb to 15th.
A stubborn Palace defence kept Harry Redknapp's side at bay on Sunday as the London rivals claimed what could prove to be a valuable point apiece in their respective battles to avoid relegation.
Palace co-chairman Steve Parish demanded a response from the club's players after the sacking of Warnock 24 hours previously, but neither side were able to make an impact over the course of a low-quality first half, although the visitors almost took the lead through Jason Puncheon.
QPR had the better of proceedings after half-time, with Leroy Fer going close with two audacious strikes, while Palace continued to provide a threat.
James McArthur made a terrific goal-line clearance from a Steven Caulker header, but both teams had to settle for a share of the spoils. The point sees QPR leapfrog above West Brom, while Palace remain in the bottom three.
Redknapp made a bold six changes to the QPR side dispatched 2-1 by 10-man Arsenal on Boxing Day, with Rio Ferdinand dropping back to the bench and replaced by Richard Dunne.
Millen, taking temporary charge of Palace for a third time, replaced the injured Fraizer Campbell with Wilfried Zaha in the visitors' only change, and both sides struggled to impose themselves during a cagey opening period.
In-form forward Charlie Austin went close after 15 minutes, testing Palace goalkeeper Julian Speroni with a rasping volley from the edge of the box in QPR's first meaningful attack.
Redknapp's men have the Premier League's worst defensive record so far in 2014-15, having conceded 34 times, and that backline was carved open six minutes later when Puncheon almost put the visitors ahead with a delightful left-footed strike that hit the post.
Palace continued to look dangerous on the counter attack, with Yannick Bolasie and Zaha both prominent, while veteran QPR defender Clint Hill was perhaps lucky to escape a red card following a reckless lunge on Adrian Mariappa.
The hosts came out strong after the restart and Fer fired an ambitious volley just wide of the upright from an acute angle after latching onto a floated cross.
Bolasie still proved a constant presence for Palace, but QPR continued to press, with Fer linking up play well in central areas.
And it was the Dutch midfielder who caused havoc again when he picked up the ball 30 yards out before unleashing a powerful drive that was destined for the top-right corner, but Speroni reacted superbly to tip it over.
But Palace were not be deterred and Bolasie should have tested Robert Green when, after doing brilliantly to latch onto a long ball from the back and shake off Mauricio Isla, the skilful winger delayed his shot, allowing Dunne to intervene.
Redknapp introduced Eduardo Vargas and Matt Phillips as QPR searched for a winner and they almost had it when Caulker rose well to meet Joey Barton's pin-point corner, but McArthur was well positioned to head clear off the line.
Junior Hoilett lashed wide as the final whistle approached, while Barton's quality set-piece deliveries put Palace under constant pressure, but the visitors held on to secure a well-earned point.