Zeki Amdouni came off the bench to rescue the Clarets a point, slotting home from 12 yards after being poleaxed by goalkeeper Andre Onana.
The Red Devils had previously been gifted a goal in the 79th minute when Antony pounced on Sander Berge’s mistake to give the hosts a lead.
But Vincent Kompany’s men were well worthy of their point and maybe might even think they deserved more.
Here’s how Burnley’s players rated:
1. Arijanet Muric - 8/10
Made three big saves, all from Antony, but couldn’t quite stretch far enough to deny the Brazilian for United’s late goal. Photo: Ash Donelon
2. Lorenz Assignon - 7/10
Made three big saves, all from Antony, but couldn’t quite stretch far enough to deny the Brazilian for United’s late goal. Photo: Matthew Peters
3. Dara O'Shea - 8/10
Defended resolutely and made some key blocks and interceptions when space was left in behind. Blazed over a decent chance at the other end. Photo: OLI SCARFF
4. Maxime Esteve - 7/10
Produced a vital block to deny Bruno Fernandes, who had been played into space behind him. Photo: OLI SCARFF