The Toffees produced an incredible comeback to beat Crystal Palace 3-2 at Goodison Park having trailed 2-0 at the interval and Frank Lampard’s side are now four points clear of the drop zone.
The battle to avoid finishing in the division’s final relegation place and joining Watford and Norwich City in being relegated is now a two-horse race between Leeds and Burnley heading into Sunday’s final day.
But United’s far inferior goal difference means that the Whites will be consigned to the drop if Burnley beat Newcastle United at Turf Moor, regardless of how Leeds fare at Brentford.
Jesse Marsch’s side are level on points with the Clarets but their goal difference is minus 38 compared to Burnley’s minus 18 so Leeds need to better Burnley’s result against the Magpies.
At Villa Park, Burnley were awarded a penalty when Emi Buendia tripped Maxwel Cornet in the box.
Ashley Barnes stepped up to take the spot-kick and sent Emi Martinez the wrong way.
Villa hit back to level just three minutes after the restart as Buendia volleyed home.
The Clarets finished the game with 10 men as substitute Matt Lowton was shown a straight red card for a late tackle on Calum Chambers.
Second-half goals from Michael Keane, Richarlison and Dominic Calvert-Lewin clinched a thrilling win for Everton.
Marcos Alonso’s volley cancelled out James Maddison’s goal as Chelsea were held 1-1 by Leicester City.