Stoke City took a big step towards survival with a rare away win that all but sealed Queens Park Rangers' fate.
The visitors took the lead just before half-time when Peter Crouch converted Cameron Jerome's cut-back.
And Jon Walters sealed the win from the penalty spot after Clint Hill had impeded Crouch.
QPR dream in tatters - Redknapp
Stoke moved up to 15th place, six points clear of the drop zone, while QPR will be relegated on Monday if Aston Villa beat Manchester United.
Livewire striker Loic Remy apart, QPR looked a disjointed unit in a match which provided ample evidence as to why they are in such a dire predicament.
Too often players shot when they should have passed and vice versa, while in conceding the opening goal shortly before the break the home side reprised a habit that has cost them points up and down the country.
Stoke had entered the match on a desperate run that had seen them slip into relegation contention, but Crouch's opener injected much-needed confidence into their play and they comfortably held on for a first away victory since 1 December.
With Stoke pressing from the off, a QPR side showing five changes from the one
beaten 2-0 at Everton last weekend
looked to threaten on the counter-attack with Adel Taarabt finding space between the visitors' midfield and defence.
Harry Redknapp has won just four of his 21 Premier League games in charge of QPR, meaning that he has a lower win percentage (19%) than both Mark Hughes and Neil Warnock as QPR boss in the competition (20%).
The Moroccan almost shaved the post with two early long-range strikes then ignored well-placed team-mates to his left and right before blazing wastefully wide.
Stoke's attacks regularly carried promise but too often broke down due to a lack of guile and poise in and around the penalty area.
Nonetheless, they were almost gifted an opener when Rob Green fumbled Walters's shot and looked on in relief as the ball bounced away to safety.
Green fared rather better when called into action to keep out a fierce long-range half-volley from Crouch that was destined for the top corner.
Just as they had against Everton, QPR fell behind just before half-time. Marc Wilson dispossessed Andros Townsend and fed Jerome, who eluded Chris Samba with some neat footwork and pulled the ball back for Crouch to put away only his second goal since September.
QPR 0-2 Stoke: Potters not safe yet - Tony Pulis
Samba almost levelled before the break as his hooked effort from a right-wing free-kick drifted fractionally wide of the far post.
With four goals in his previous six starts, Remy represented QPR's best hope and the Frenchman almost delivered an equaliser when he wriggled past a couple of Stoke defenders inside the box and fired a left-footed shot that was well saved by Asmir Begovic, diving to his left.
From the resulting corner, Samba's goal-bound effort was unwittingly kept out by team-mate Stephane Mbia.
With gaps opening up in the QPR backline, Stoke came close to making it 2-0. Steven N'Zonzi's cross from the left found its way to Charlie Adam at the far post, but the Scot's cushioned effort looped over the bar.
It was no surprise when the second goal arrived 15 minutes before full-time. After Robert Huth's header had struck a post, Crouch was pulled down by Hill as he looked to convert the rebound and referee Chris Foy pointed to the spot.
Stoke's Premier League run-in
27 April: Norwich (h)
6 May: Sunderland (a)
12 May: Tottenham (h)
19 May: Southampton (a)
Walters, who had missed two of his previous four penalties this season, was forced to take his effort twice because of encroaching players but held his nerve to drill the ball into the bottom corner.
QPR fashioned little by way of response and must surely now start planning for life in the Championship next season.
Stoke manager Tony Pulis:
"They are very good on the break and we got caught four or five times. It was great for Peter to score before half-time and in the second half we tightened up and were a lot better.
"It takes a bit of pressure off but there is still pressure there and the four games we'll play are very tough games.
"40 points will be enough because we have good goal difference. There is still work to be done. A win or three draws, I don't care how we cook it."
Full Time The final whistle goes and the game is over.
Shaun Derry gives away a free kick for an unfair challenge on Steven Nzonzi. Asmir Begovic takes the direct free kick.
Dean Whitehead is caught offside. Rob Green takes the free kick.
Substitution Geoff Cameron on for Peter Crouch.
The referee blows for offside. Free kick taken by Asmir Begovic.
David Hoilett fouled by Andy Wilkinson, the ref awards a free kick. Tal Ben Haim delivers the ball from the free kick right-footed from left wing, Asmir Begovic makes a save.
The referee blows for offside. Free kick taken by Asmir Begovic.
Cameron Jerome gives away a free kick for an unfair challenge on Clint Hill. Tal Ben Haim takes the direct free kick.
Free kick awarded for a foul by Ryan Shotton on Jay Bothroyd. Jose Bosingwa takes the free kick.
Dean Whitehead takes the outswinging corner, Headed effort from deep inside the area by Robert Huth misses to the left of the goal.
Unfair challenge on Peter Crouch by Stephane Mbia results in a free kick. Direct free kick taken by Glenn Whelan.
Shaun Derry takes a shot from just inside the penalty box which clears the bar.
Direct strike on goal from the free kick comes in from Jay Bothroyd, blocked by Glenn Whelan.
Booking Steven Nzonzi receives a yellow card.
Steven Nzonzi gives away a free kick for an unfair challenge on David Hoilett.
The assist for the goal came from Peter Crouch.
76:14 Goal scored
Goal! - Jonathan Walters - QPR 0 - 2 Stoke Power penalty scored by Jonathan Walters. QPR 0-2 Stoke.
Booking Clint Hill is given a yellow card.
Clint Hill challenges Peter Crouch unfairly and gives away a Penalty.
Free kick awarded for a foul by David Hoilett on Dean Whitehead. Glenn Whelan crosses the ball, Header from close range by Robert Huth strikes the post.
Jose Bosingwa crosses the ball, save by Asmir Begovic.
Free kick awarded for an unfair challenge on Jay Bothroyd by Cameron Jerome. Jose Bosingwa produces a cross, Christopher Samba takes a shot. Save by Asmir Begovic.
Substitution Dean Whitehead joins the action as a substitute, replacing Charlie Adam.
Shot from just outside the area by David Hoilett goes over the bar.
Corner taken by Glenn Whelan from the left by-line, Christopher Samba makes a clearance.
Effort from outside the box by Peter Crouch goes wide right of the target.
Shot by Jay Bothroyd from outside the box goes over the target.
Close range effort by Charlie Adam goes over the bar.
Jay Bothroyd fouled by Ryan Shotton, the ref awards a free kick. Jose Bosingwa takes the direct free kick.
David Hoilett takes the inswinging corner, clearance made by Glenn Whelan.
Substitution (Stoke) makes a substitution, with Andy Wilkinson coming on for Marc Wilson.
Free kick awarded for an unfair challenge on Charlie Adam by Tal Ben Haim. Free kick taken by Charlie Adam.
Shot from a long way out by Charlie Adam goes wide of the left-hand upright.
Stephane Mbia is flagged offside by the assistant referee. Asmir Begovic restarts play with the free kick.
Shot by Christopher Samba from 6 yards.
Corner taken by Jose Bosingwa from the left by-line.
Substitution Jay Bothroyd replaces Adel Taarabt.
Loic Remy takes a shot. Save by Asmir Begovic.
Outswinging corner taken right-footed by Jose Bosingwa, clearance by Ryan Shawcross.
Shot from deep inside the area by Ryan Shawcross goes over the bar.
Corner taken right-footed by Glenn Whelan from the left by-line, Christopher Samba makes a clearance.
Loic Remy is caught offside. Asmir Begovic takes the free kick.
Peter Crouch is adjudged to have handled the ball. Rob Green takes the free kick.
Free kick awarded for an unfair challenge on Marc Wilson by Jamie Mackie. Marc Wilson restarts play with the free kick.
The referee starts the second half.
Substitution Andros Townsend leaves the field to be replaced by Jamie Mackie.
45:00 +3:13 Half time
Half Time The referee blows for half time.
Andros Townsend takes a shot. Blocked by Jonathan Walters.
Free kick awarded for an unfair challenge on Andros Townsend by Marc Wilson. The ball is delivered by Jose Bosingwa, Christopher Samba produces a right-footed shot from deep inside the penalty area which goes wide of the left-hand post.
Assist by Cameron Jerome.
41:34 Goal scored
Goal! - Peter Crouch - QPR 0 - 1 Stoke Goal scored by Peter Crouch from inside the six-yard box to the bottom left corner of the goal. QPR 0-1 Stoke.
Stephane Mbia has a shot on goal from long range that goes wide left.
Charlie Adam fouled by Loic Remy, the ref awards a free kick. Free kick taken by Asmir Begovic.
Effort on goal by Adel Taarabt from deep inside the area goes harmlessly over the bar.
Glenn Whelan challenges Adel Taarabt unfairly and gives away a free kick. Strike on goal comes in from Loic Remy from the free kick, blocked by Marc Wilson.
Stephane Mbia takes a shot. Blocked by Ryan Shawcross.
Charlie Adam takes the chance to get an effort at goal.
David Hoilett has shot on goal from just outside the box which goes wide of the right-hand upright.
Andros Townsend takes a shot and went wide right of the goal.
Unfair challenge on Stephane Mbia by Charlie Adam results in a free kick. Tal Ben Haim restarts play with the free kick.
Ryan Shawcross gives away a free kick for an unfair challenge on Loic Remy. Jose Bosingwa has an effort direct from the free kick, save by Asmir Begovic.
Charlie Adam takes the inswinging corner, clearance by Clint Hill.
Volleyed right-footed shot by Peter Crouch. Save made by Rob Green.
Shot from just outside the area by Loic Remy misses to the right of the target.
Andros Townsend has a shot on goal from outside the area which misses left.
Clint Hill challenges Cameron Jerome unfairly and gives away a free kick. Free kick taken by Peter Crouch.
Jonathan Walters takes a shot. Save by Rob Green.
Loic Remy takes a shot. Save by Asmir Begovic.
Loic Remy takes a shot. Save made by Asmir Begovic.
Direct free kick taken by Christopher Samba.
Booking Charlie Adam is cautioned.
Free kick awarded for an unfair challenge on Loic Remy by Charlie Adam.
Loic Remy is penalised for handball and concedes a free kick. Free kick taken by Asmir Begovic.
Outswinging corner taken right-footed by Adel Taarabt, Loic Remy takes a shot. Blocked by Ryan Shotton.
Unfair challenge on Tal Ben Haim by Peter Crouch results in a free kick. Rob Green takes the direct free kick.
Adel Taarabt has an effort at goal from just outside the box which goes wide of the right-hand upright.
Shot by Ryan Shawcross. Blocked by Christopher Samba.
Adel Taarabt takes a short corner.
Free kick awarded for a foul by Robert Huth on Adel Taarabt. Free kick crossed right-footed by Jose Bosingwa, clearance made by Robert Huth.
Steven Nzonzi gives away a free kick for an unfair challenge on Adel Taarabt. Adel Taarabt produces a shot on goal direct from the free kick.
Inswinging corner taken by Glenn Whelan from the left by-line, Rob Green makes a save.
Shot by Andros Townsend from outside the area goes high over the crossbar.
Effort from outside the penalty box by Adel Taarabt goes wide right of the goal.
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