Burnley ran out 4-1 winners at Sheffield United in the battle of the bottom two to throw themselves a Premier League lifeline.
Jacob Bruun Larsen and Lorenz Assignon struck in the space of two minutes and against the run of play at the end of the first half, before the Blades threatened a comeback when Gus Hamer pulled one back early in the second.
But further goals from Lyle Foster and substitute Johann Berg Gudmundsson crushed the Blades’ hopes as Burnley maintained their late bid for survival.
Vincent Kompany’s side have now taken 10 points from their last seven matches and climbed to within three points of 17th-placed Nottingham Forest, who play at relegation rivals Everton on Sunday.
Blades boss Chris Wilder said this week he wanted his side to extend their survival fight for as long as possible and they created the better first-half chances.
Oli McBurnie’s close-range effort was well saved by Burnley goalkeeper Arijanet Muric, who rescued his side again when parrying Ben Brereton Diaz’s shot.
McBurnie’s rising drive then drew another save from Muric, but against the run of play, the visitors struck twice in two minutes as the interval approached to stun Bramall Lane.
Wilson Odobert’s weaving run to the edge of the area had the Blades back-pedalling and when his blocked shot rebounded to Bruun Larsen, the latter’s low scuffed effort deflected off Jayden Bogle and span inside the near post.
Blades goalkeeper Ivo Grbic had been caught off balance by the ricochet and he was left flat-footed again two minutes later.
Assignon darted in between Ben Osborn and Brereton Diaz on the right edge of the area and his toe-poked shot went through Auston Trusty’s legs and flew high into the net off Grbic’s out-stretched boot for his first Burnley goal.
The Blades went close to reducing their two-goal deficit at the start of the second period when James McAtee’s goalbound shot was brilliantly saved by Muric and the hosts were back in it in the 52nd minute.
Hamer cut inside Assignon on the left edge of the area and curled a superb right-footed finish inside the far post.
Muric denied Brereton Diaz an equaliser with another top-class save before the home side’s fightback hopes were dealt a mighty blow.
Assignon marauded down the right and picked out Foster with a low ball into the box and the striker made no mistake from six yards.
McBurnie fired narrowly wide as the Blades continued to press forward, but they were stung again in the 71st minute when Gudmundsson curled home a fine finish less than a minute after stepping off the bench to replace Vitinho.
Gudmundsson then rattled a post and with Blades fans leaving in their hordes, the Clarets comfortably saw out just their second win of the year.
