Everton scored either side of half-time to maintain their European challenge and push Queens Park Rangers closer to relegation from the Premier League.
The visitors were in the ascendancy when Loic Remy's shot was saved by Tim Howard after Junior Hoilett's early curler fizzed just wide.
But five minutes before the break, Darron Gibson's shot was cruelly deflected off Clint Hill on its way in.
Redknapp critical of 'sloppy' QPR
And, after Everton improved, Victor Anichebe flicked in following a corner.
For periods in the first half it looked as though QPR might continue their three-game unbeaten run against the Toffees since their return to the top flight in May 2011.
But the manner in which they went behind understandably stripped them of confidence and their position looks ever more parlous with only five games remaining.
Harry Redknapp's side remain seven points from safety, but they have now played two more games than their closest relegation rivals Wigan and one more than Sunderland, who face Newcastle on Sunday.
With Rangers having won only four league games all season, Redknapp targeted as many victories again from their final six games, but the prospect of survival must now look even more remote.
Queens Park Rangers have conceded 13 goals from corner situations this season, at least five more than any other team.
Following Arsenal's win over Norwich, David Moyes's Everton stay sixth in the table and face a crucial game against the Gunners on Tuesday. They are still in the hunt for a Champions League spot, as they sit just three points below fourth-placed Chelsea, who have a game in hand.
Everton recorded their fourth consecutive home win but it was QPR who twice came close to permeating the home defence before Gibson's fortunate opener.
When Park Ji-sung laid the ball off to Hoilett, the Canadian's curling shot was a whisker wide before Remy's fierce drive was palmed away by Howard.
The hosts were frustrated by what they thought was some rough-house QPR defending, and with Steven Pienaar back in the side their only real threat came when the South African combined with Leighton Baines down Everton's left.
QPR's Premier League run-in
20 April: Stoke (h)
28 April: Reading (a)
4 May: Arsenal (h)
12 May: Newcastle (h)
19 May: Liverpool (a)
Despite Sylvain Distin's off-target effort, QPR withstood Everton's laboured forays and were unlucky to concede the opening goal.
Baines crossed low for Kevin Mirallas and, when the Belgian's effort came back to Gibson, his shot cannoned in off the luckless Hill for the Irishman's second Everton goal.
Coming six days after his side conceded a crucial injury-time equaliser against Wigan, Redknapp looked absolutely sick on the sidelines and with some justification.
Problems then mounted for his side as Everton emerged after the break as a completely different proposition.
They were far quicker to the ball and passed with extra vitality as they conjured a number of chances, putting QPR under pressure from a succession of corners.
Moyes praises 'important' Everton win
Mirallas tricked his way past Nedum Onuoha and crossed low to Anichebe but the Nigerian smacked his shot against the post from eight yards.
He made up for that miss, though, when he flicked in Distin's header from another accurate Baines corner.
It was no more than Everton deserved and they could have made the scoreline more comfortable when Mirallas twice had shots saved by Julio Cesar.
Onuoha had a solitary effort for QPR as the game petered out miserably for them. With few chances to make amends now, their season could go the same way.
Everton boss David Moyes on Darron Gibson's goal:
"He should do more but he has a thigh problem and we were nearly having to take him off. We think he will need an operation at end of the season so he has been reticent to shoot and take things on but it got a big deflection which helped us as well.
"It's a really important three points, I was worried about today's game. QPR have a lot to play for but they are nearly getting to a situation where there's not much to play for.
"I think if we beat Arsenal in midweek we can talk about the Champions League but if we lose we are more talking about trying, if possible, to finish in that Europa League place."
QPR manager Harry Redknapp:
"It was another blow, last week was a massive blow at home to Wigan. Everton is always a difficult place to come but at half-time I thought we were unfortunate to be 1-0 down.
"The goal was a massive deflection and we came in at half-time feeling sorry for ourselves.
"You have to keep going, you can't suddenly feel sorry for ourselves… but we started sloppy and became undisciplined, we didn't do our jobs properly, we gave free-kicks away, we kicked the ball away, we got bookings. It didn't do us any favours.
"I can't stand there and go no [we can't survive], if it's a no I may as well go on holiday now.
"We have to believe, we have to beat Stoke, we have to go to Reading and win, we have to win the other two home games against Newcastle and Arsenal. I know it's tough and it's going to be very difficult but while you've got a chance you have to keep going."
Full Time The referee signals the end of the game.
The official flags Nikica Jelavic offside. Christopher Samba restarts play with the free kick.
Tim Howard takes the direct free kick.
90:00 +1:44 Substitution
Substitution (Everton) makes a substitution, with Johnny Heitinga coming on for Victor Anichebe.
Sylvain Distin fouled by Christopher Samba, the ref awards a free kick.
Victor Anichebe gives away a free kick for an unfair challenge on Andros Townsend. Jose Bosingwa restarts play with the free kick.
Andros Townsend has an effort at goal from long range that misses to the right of the target.
Victor Anichebe takes a shot. Blocked by Nedum Onuoha.
Free kick taken by Tim Howard.
Substitution Steven Naismith comes on in place of Kevin Mirallas.
Corner taken right-footed by Adel Taarabt, Phil Jagielka makes a clearance. Clint Hill concedes a free kick for a foul on Phil Jagielka.
Darron Gibson takes a shot. Blocked by Adel Taarabt. Kevin Mirallas decides to take the corner short.
The referee blows for offside. Tim Howard takes the indirect free kick.
Adel Taarabt takes a shot. Marouane Fellaini gets a block in.
Substitution Nikica Jelavic joins the action as a substitute, replacing Leon Osman.
Nedum Onuoha takes a shot. Tim Howard makes a save.
Loic Remy sends in a cross, save by Tim Howard.
Direct free kick taken by Jose Bosingwa.
Booking Darron Gibson is shown a yellow card for unsporting behaviour.
Darron Gibson gives away a free kick for an unfair challenge on Adel Taarabt.
Centre by Kevin Mirallas, save by Soares Julio Cesar.
Inswinging corner taken right-footed by Adel Taarabt from the left by-line to the near post, clearance by Marouane Fellaini.
Substitution Esteban Granero leaves the field to be replaced by Samba Diakite.
Victor Anichebe takes a shot. Blocked by Clint Hill.
Free kick awarded for a foul by Clint Hill on Marouane Fellaini. Direct free kick taken by Leighton Baines.
Adel Taarabt has shot on goal from just outside the area which goes wide of the right-hand upright.
Kevin Mirallas takes a shot. Save by Soares Julio Cesar.
Corner taken by Kevin Mirallas from the left by-line, Sylvain Distin takes a shot. Soares Julio Cesar makes a save.
The offside flag is raised against Christopher Samba. Tim Howard takes the indirect free kick.
Free kick taken by Esteban Granero.
Substitution Adel Taarabt on for Ji-Sung Park.
Booking Booking for Steven Pienaar for unsporting behaviour.
Ji-Sung Park fouled by Steven Pienaar, the ref awards a free kick.
Sylvain Distin provided the assist for the goal.
55:14 Goal scored
Goal! - Victor Anichebe - Everton 2 - 0 QPR Goal scored by Victor Anichebe from inside the six-yard box low into the middle of the goal. Everton 2-0 QPR.
Sylvain Distin takes a shot.
Inswinging corner taken by Leighton Baines,
Kevin Mirallas fouled by Esteban Granero, the ref awards a free kick. Free kick crossed by Leighton Baines, clearance by Nedum Onuoha.
Corner taken by Kevin Mirallas from the left by-line to the near post, clearance made by Andros Townsend.
Booking Andros Townsend is cautioned.
Phil Jagielka takes a shot.
Inswinging corner taken by Leighton Baines, save by Soares Julio Cesar.
Inswinging corner taken by Leighton Baines from the right by-line played to the near post, Nedum Onuoha makes a clearance.
Free kick crossed left-footed by Leighton Baines, Esteban Granero makes a clearance.
Booking Esteban Granero receives a yellow card for dissent.
Esteban Granero concedes a free kick for a foul on Darron Gibson.
Inswinging corner taken left-footed by Leighton Baines from the right by-line, Sylvain Distin takes a shot. Save made by Soares Julio Cesar. Kevin Mirallas decides to take a short corner.
Victor Anichebe takes a shot. Save by Soares Julio Cesar.
Loic Remy takes a shot. Save made by Tim Howard.
The referee gets the second half underway.
45:00 +1:11 Half time
Half Time The match has reached half-time.
The ball is swung over by Leighton Baines, save by Soares Julio Cesar.
The official flags Loic Remy offside. Free kick taken by Phil Jagielka.
The referee blows for offside against Kevin Mirallas. Soares Julio Cesar takes the indirect free kick.
The assist for the goal came from Kevin Mirallas.
39:47 Goal scored
Goal! - Darron Gibson - Everton 1 - 0 QPR Darron Gibson fires in a goal from outside the penalty box to the bottom right corner of the goal. Everton 1-0 QPR.
Kevin Mirallas takes a shot. Esteban Granero gets a block in.
Corner taken by Leighton Baines from the left by-line to the near post, clearance by Clint Hill.
Direct free kick taken by Esteban Granero.
Booking Marouane Fellaini is cautioned by the ref for unsporting behaviour.
Leighton Baines takes the free kick. Darron Gibson takes a shot. Sylvain Distin has an effort at goal from deep inside the area missing to the left of the target. Unfair challenge on Jermaine Jenas by Marouane Fellaini results in a free kick.
Booking The referee shows Jose Bosingwa a yellow card.
Foul by Jose Bosingwa on Seamus Coleman, free kick awarded.
Corner taken by Kevin Mirallas played to the near post.
Short corner taken by Kevin Mirallas.
Free kick awarded for an unfair challenge on Steven Pienaar by Andros Townsend. Leighton Baines takes the free kick.
Corner taken left-footed by Leighton Baines from the left by-line, clearance made by Clint Hill.
Jermaine Jenas is caught offside. Free kick taken by Tim Howard.
Corner taken right-footed by Esteban Granero to the near post, clearance by Darron Gibson.
Loic Remy takes a shot. Tim Howard makes a save. Short corner worked by Andros Townsend.
Loic Remy takes a shot.
Free kick awarded for an unfair challenge on Esteban Granero by Steven Pienaar. Free kick taken by Esteban Granero.
Loic Remy gives away a free kick for an unfair challenge on Seamus Coleman. Free kick taken by Darron Gibson.
David Hoilett produces a cross, save by Tim Howard.
Loic Remy is flagged offside by the assistant referee. Free kick taken by Phil Jagielka.
Unfair challenge on Seamus Coleman by David Hoilett results in a free kick. Tim Howard takes the direct free kick.
Free kick awarded for a foul by Andros Townsend on Steven Pienaar. Sylvain Distin takes the direct free kick.
Corner taken by Leighton Baines played to the near post, save by Soares Julio Cesar.
Esteban Granero takes the inswinging corner, clearance made by Darron Gibson.
Leighton Baines delivers the ball.
Seamus Coleman delivers the ball.
The referee blows for offside against Loic Remy. Indirect free kick taken by Phil Jagielka.
Loic Remy is ruled offside. Phil Jagielka restarts play with the free kick.
David Hoilett has an effort at goal from just outside the box which goes wide of the right-hand upright.
Free kick awarded for a foul by Marouane Fellaini on Esteban Granero. Free kick taken by Clint Hill.
Jose Bosingwa gives away a free kick for an unfair challenge on Steven Pienaar. Free kick crossed left-footed by Leighton Baines from left wing.
Ji-Sung Park challenges Leon Osman unfairly and gives away a free kick. Direct free kick taken by Darron Gibson.
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