Portsmouth's survival hopes were dented after Burnley's Charlie Austin scored a hat-trick to leave them five points from safety.
Kieran Trippier gave the visitors an early lead before David Norris equalised from close range for Pompey.
But Danny Ings' header just after the break gave Burnley the lead before substitute Austin made it 3-1.
Austin scored two goals in the dying moments, his third from inside the area to the top left corner of the goal.
It is looking increasingly bleak for Portsmouth, five points adrift of safety with six games remaining.
They had gone into the match buoyed by two consecutive home wins but had no answer to Burnley's excellent second-half showing.
Portsmouth's remaining games
07 April: A v Southampton
10 April: H v Millwall
14 April: A v Doncaster
17 April: H v Crystal Palace
21 April : H v Derby
28 April : A v Nottingham Forest
The Clarets took the lead in the 16th minute when Dean Marney's low corner from the left flank was dummied to Trippier, who found the net with a sweetly-struck drive into the bottom corner from 25 yards.
Portsmouth's response was swift and clinical.
Luke Varney scampered onto George Thorne's searching pass down the right wing and cut the ball across goal for Norris to thump into the roof of the net.
But the visitors scored four times after the interval, Austin finding the net three times in the final 16 minutes.
Burnley were back in front two minutes after the restart courtesy of Ings's glancing header.
Austin was introduced in the 53rd minute when fellow striker Martin Paterson appeared to suffer a hamstring strain.
And the former Swindon player made it 3-1 in the 74th minute after a free-kick by Ross Wallace had caused panic in the Portsmouth defence.
An under-hit backpass from Pompey defender Jason Pearce gifted Austin his 50th career goal in stoppage time.
And Burnley fans were still celebrating when the 22-year-old completed his hat-trick from close range.
Portsmouth manager Michael Appleton said: "I do not mind if it it goes down to the last day as long as we stay up.
"I am still confident but it was a big blow to lose.
"I felt we dominated the first period but they came back into it and were a lot better than us in the second half. I was disappointed with that."
Burnley manager Eddie Howe said: "I think we have the best strikers in the Championship.
We have Charlie [Austin], Jay [Rodriguez], Danny [Ings] who are all top quality forwards.
"They are all very clinical and they showed that.
"Portsmouth dominated the first half, but I thought we were excellent in the second period."
- 01 Ashdown
- 02 Ward (Etuhu - 69' )
- 05 Pearce
- 15 Halford
- 23 Rekik
- 26 Ben-Haim
- 16 Allan (Futacs - 69' Booked )
- 19 Norris Booked
- 20 Thorne (Scapuzzi - 81' )
- 11 Varney
- 22 Maguire Booked
- 03 Rocha
- 17 Harris
- 09 Futacs
- 14 Etuhu
- 24 Scapuzzi
- 01 Grant Booked
- 02 Trippier
- 04 Duff
- 15 Edgar
- 36 Mee (McQuoid - 71' )
- 06 McCann
- 07 Wallace
- 08 Marney Booked
- 20 Bartley
- 10 Paterson (Austin - 52' Booked )
- 14 Ings (Stanislas - 90' )
- 12 Jensen
- 11 Stanislas
- 19 McQuoid
- 23 Austin
- 32 Hayieson
Live Text Commentary
Full Time The referee blows his whistle to end the game.90:00 +5:26
Josh McQuoid provided the assist for the goal.90:00 +5:26 Goal scored
Goal! - Charlie Austin - Portsmouth 1 - 5 Burnley Charlie Austin fires in a goal from inside the penalty box to the top left corner of the goal. Portsmouth 1-5 Burnley.90:00 +5:15
The ball is sent over by Tal Ben-Haim, Kieran Trippier manages to make a clearance.90:00 +3:49 Substitution
Substitution (Burnley) makes a substitution, with Junior Stanislas coming on for Danny Ings.90:00 +3:29 Booking
Booking Booking for Charlie Austin for unsporting behaviour.90:00 +2:40 Goal scored
Goal! - Charlie Austin - Portsmouth 1 - 4 Burnley Goal scored by Charlie Austin from close in to the bottom left corner of the goal. Portsmouth 1-4 Burnley.90:00 +1:46
Luca Scapuzzi concedes a free kick for a foul on Lee Grant. Direct free kick taken by Lee Grant.90:00 +0:58
Free kick awarded for a foul by Ross Wallace on Chris Maguire. Direct free kick taken by Chris Maguire.90:00 +0:17
Josh McQuoid takes a shot. Jamie Ashdown makes a save.88:52
Karim Rekik fouled by David Edgar, the ref awards a free kick. Jamie Ashdown restarts play with the free kick.85:51
Chris Maguire takes the inswinging corner, clearance made by Josh McQuoid.85:43
David Norris takes a shot. Kieran Trippier gets a block in.83:48
Marvin Bartley concedes a free kick for a foul on Luca Scapuzzi. Free kick taken by Jamie Ashdown.83:15 Booking
Booking The referee cautions David Norris for unsporting behaviour.83:00
Kieran Trippier takes a shot. Blocked by Jason Pearce.82:23
The ball is delivered by Ross Wallace, Jason Pearce manages to make a clearance.81:37
A cross is delivered by Chris McCann, save by Jamie Ashdown.80:44 Substitution
Substitution Luca Scapuzzi comes on in place of George Thorne.80:36
Effort from inside the area by David Norris misses to the left of the target.
The referee blows for offside. Lee Grant restarts play with the free kick.77:59
Direct free kick taken by Kieran Trippier.77:59 Booking
Booking Dean Marney receives a caution.77:55 Booking
Booking The referee books Chris Maguire for unsporting behaviour.77:18 Booking
Booking The referee books Marko Futacs for unsporting behaviour.77:10
Marko Futacs challenges Danny Ings unfairly and gives away a free kick.76:52
Charlie Austin takes a shot. Blocked by George Thorne.76:09
Foul by David Norris on Marvin Bartley, free kick awarded. Direct free kick taken by Kieran Trippier.75:48
The ball is delivered by Josh McQuoid, clearance by Tal Ben-Haim.74:17
The official flags Marko Futacs offside. Free kick taken by Lee Grant.73:12
Assist on the goal came from Ross Wallace.73:12 Goal scored
Goal! - Charlie Austin - Portsmouth 1 - 3 Burnley Charlie Austin gets on the score sheet with a goal from inside the six-yard box to the bottom left corner of the goal. Portsmouth 1-3 Burnley.72:49
Josh McQuoid fouled by Tal Ben-Haim, the ref awards a free kick. Ross Wallace restarts play with the free kick.72:11
The ball is delivered by Kelvin Etuhu, Close range headed effort by Luke Varney goes wide of the left-hand upright.71:43
Chris Maguire fouled by David Edgar, the ref awards a free kick. Tal Ben-Haim restarts play with the free kick.71:12
Tal Ben-Haim gives away a free kick for an unfair challenge on Chris McCann. Lee Grant restarts play with the free kick.70:19 Substitution
Substitution Josh McQuoid replaces Ben Mee.68:33 Substitution
Substitution Marko Futacs on for Scott Allan.68:33 Substitution
Substitution Kelvin Etuhu joins the action as a substitute, replacing Joel Ward.64:54
Charlie Austin delivers the ball.63:55
David Norris produces a left-footed shot from just outside the box that goes wide left of the goal.60:42
Outswinging corner taken from the right by-line by Scott Allan, Lee Grant fouled by Jason Pearce, the ref awards a free kick. Lee Grant takes the direct free kick.60:16
Ben Mee challenges Scott Allan unfairly and gives away a free kick. Free kick taken by Tal Ben-Haim.59:29 Booking
Booking Lee Grant receives a caution for time wasting.58:51
Unfair challenge on David Edgar by Chris Maguire results in a free kick. Direct free kick taken by Lee Grant.55:06
Corner taken right-footed by Scott Allan, George Thorne produces a right-footed shot from just outside the area that goes wide left of the goal.54:26
The referee penalises David Edgar for handball. Free kick taken by Greg Halford.53:34
Luke Varney produces a right-footed shot from deep inside the penalty box which goes wide of the right-hand upright.52:37
Kieran Trippier produces a cross, Tal Ben-Haim manages to make a clearance.51:31 Substitution
Substitution Martin Paterson goes off and Charlie Austin comes on.49:02
The referee penalises Luke Varney for handball. Lee Grant takes the free kick.47:34
Corner taken right-footed by Scott Allan from the left by-line, David Norris produces a right-footed shot from deep inside the area which goes wide of the left-hand post.47:18
The ball is delivered by Scott Allan, clearance by Kieran Trippier.46:13
David Edgar provided the assist for the goal.46:13 Goal scored
Goal! - Danny Ings - Portsmouth 1 - 2 Burnley Danny Ings finds the net with a headed goal from close range. Portsmouth 1-2 Burnley.45:39
Corner from the left by-line taken by Kieran Trippier, clearance made by Greg Halford.45:26
Chris McCann produces a cross, blocked by George Thorne.45:01
The second half begins.45:00 +3:07 Half time
Half Time The match has reached half-time.45:00 +1:14
The ball is swung over by Karim Rekik, clearance by Michael Duff.45:00 +0:31
David Edgar takes a shot. Tal Ben-Haim gets a block in.45:00 +0:05
Inswinging corner taken by Ross Wallace from the right by-line.44:42
Ben Mee takes a shot. Save made by Jamie Ashdown.42:06
Corner taken by Scott Allan from the right by-line.41:31
Chris Maguire takes a shot. Save by Lee Grant.36:28
Scott Allan sends in a cross, Kieran Trippier manages to make a clearance.35:07
A cross is delivered by Chris Maguire.33:25
Martin Paterson is flagged offside by the assistant referee. Tal Ben-Haim takes the indirect free kick.31:57
Shot by Martin Paterson from deep inside the penalty area misses wide to the left of the target.30:45
Greg Halford has an effort at goal from deep inside the area missing to the right of the goal.27:42
The ball is sent over by Chris Maguire, save by Lee Grant.26:03
The referee blows for offside against Martin Paterson. Indirect free kick taken by Jamie Ashdown.25:31
Scott Allan gives away a free kick for an unfair challenge on Danny Ings. Free kick taken by Ben Mee.24:45
Greg Halford crosses the ball.24:29
Tal Ben-Haim produces a cross, clearance by Ben Mee.22:30
Centre by Luke Varney.20:42
Effort on goal by Chris McCann from just outside the area goes harmlessly over the target.18:24
Assist by Luke Varney.18:24 Goal scored
Goal! - David Norris - Portsmouth 1 - 1 Burnley A goal is scored by David Norris from inside the six-yard box to the top left corner of the goal. Portsmouth 1-1 Burnley.17:08
Foul by Luke Varney on Ben Mee, free kick awarded. Lee Grant takes the free kick.16:45
Corner taken by Scott Allan from the left by-line, save by Lee Grant.15:41
Dean Marney provided the assist for the goal.15:41 Goal scored
Goal! - Kieran Trippier - Portsmouth 0 - 1 Burnley Kieran Trippier finds the net with a goal from inside the penalty box to the bottom right corner of the goal. Portsmouth 0-1 Burnley.14:49
Dean Marney takes a short corner,14:04
Short corner taken by Scott Allan.13:23
Outswinging corner taken by Scott Allan from the right by-line.12:53
Scott Allan takes a outswinging corner from the right by-line to the near post, clearance made by Ross Wallace.12:40
Tal Ben-Haim crosses the ball, save by Lee Grant.11:11
Ben Mee concedes a free kick for a foul on Chris Maguire. Scott Allan takes the direct free kick.10:39
Header from deep inside the area by Ben Mee goes harmlessly over the crossbar.9:58
Foul by Greg Halford on Marvin Bartley, free kick awarded. Ross Wallace restarts play with the free kick.9:16
The ball is swung over by Tal Ben-Haim.7:46
Unfair challenge on Chris McCann by Chris Maguire results in a free kick. Lee Grant takes the free kick.7:33
The ball is delivered by Tal Ben-Haim, David Edgar manages to make a clearance.5:51
Free kick awarded for a foul by George Thorne on Martin Paterson. Free kick taken by Ross Wallace.5:16
David Edgar challenges Luke Varney unfairly and gives away a free kick. Tal Ben-Haim takes the direct free kick.4:07
Martin Paterson takes a shot. Greg Halford gets a block in.2:42
Chris Maguire is caught offside. Lee Grant takes the indirect free kick.1:01
Scott Allan crosses the ball, clearance made by Kieran Trippier.0:00
The ref blows the whistle to start the match.
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