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
A v Southampton
H v Millwall
A v Doncaster
H v Crystal Palace
: H v Derby
: 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."
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