Wes Morgan headed a 90th-minute winner as Leicester City won 2-1 in the Premier League at Burnley despite Harry Maguire's early red card.
Maguire's dismissal gave Burnley the advantage at a blustery Turf Moor on Saturday but Leicester led through James Maddison's fine free-kick.
Dwight McNeil soon hit back for the Clarets, who had strong penalty appeals rejected when Charlie Taylor went down under Wilfred Ndidi's challenge.
But it was Leicester who snatched all three points as Morgan - who came on to replace Demarai Gray after Maguire saw red - overpowered James Tarkowski to nod home.
Leicester were down to 10 in the fourth minute, Maguire getting the wrong side of Johann Gudmundsson as he ran through from Jack Cork's pass, the England defender tripping his man.
Gudmundsson hit the angle with the resulting free-kick, but Burnley struggled to make their advantage count and Harvey Barnes rifled narrowly wide at the other end.
Leicester took the lead in the 33rd minute, Tarkowski bringing down Maddison on the edge of the penalty area and the midfielder bending a brilliant free-kick beyond Tom Heaton, but Burnley were soon level.
Jonny Evans gave the ball away and Burnley worked the ball to their left, McNeil and Taylor combining for the former to sweep a first-time finish across Kasper Schmeichel.
Cork and Ashley Westwood wasted openings as Burnley made a strong start to the second half, with Chris Wood only able to direct McNeil's deflected low centre over the crossbar.
Michael Oliver bizarrely opted not to point to the spot when Ndidi tripped Taylor in the box and McNeil curled a drive narrowly over as Dyche's men pressed hard for the winner.
But they were caught out in the final minute, a half-cleared corner sent back into the box by Youri Tielemans for Morgan to nod home a downward header, with Schmeichel making a huge late save to prevent substitute Matej Vydra earning the Clarets a draw.
What does it mean? Nervy times at Turf Moor
After three losses in a row, Burnley had slipped to only two points clear of the bottom three. Maguire's red card handed them an ideal opportunity to get back to winning ways but they could not make the man advantage count and their position now looks perilous ahead of the run-in.
Oliver's decision not to award a penalty for what seemed a clear foul on Taylor could be crucial as the Clarets face Chelsea, Manchester City and Arsenal in their last four league games, while further appeals for spot-kicks after the ball twice struck Morgan on the arm were rejected before the experienced defender headed the winner.
McNeil justifies U21 call
In a long slog of a season for Burnley, 19-year-old winger McNeil has been a real bright spark.
His second Premier League goal was superbly taken and Wood should have put the Clarets ahead from McNeil's cross, the youngster again his team's shining light after being called up to England's Under-21 squad for the first time this week.
Maguire slow off the mark
Leicester defender Maguire was not trying to bring Gudmundsson down, but as soon as the Iceland winger ran clear the result was only ever likely to be either a red card or a goal.
With the benefit of hindsight, Maguire perhaps should have let Gudmundsson go through on Schmeichel's goal and backed the goalkeeper to make a save, although defensive colleague Morgan got him off the hook with his late impact.
Burnley will hope for better luck in their next game, Dyche's side at home again after the international break with Wolves heading to Turf Moor. Bournemouth are the visitors to Brendan Rodgers' Leicester on March 30 as the final stretch of the season starts.