Zeki Amdouni’s 36th-minute strike looked like seeing Burnley complete the double over Rob Edwards’ side, but Morris headed home Alfie Doughty’s cross in the second minute of stoppage-time.

Celebrations were muted as Burnley appealed for what looked like a foul on Clarets goalkeeper James Trafford But referee Tony Harrington was unmoved and after a lengthy check from video assistant referee Peter Bankes, the goal stood, much to the fury of the home fans.

Up until that moment, Burnley had been good value for a win that would have left it one point behind the Hatters and two behind 17th-placed Everton, which hosts Aston Villa on Monday (AEDT), but its failure to hang on could be hugely costly come the end of the season.

Amdouni’s strike may have taken a deflection off Johann Berg Gudmundsson as it beat Thomas Kaminski on the line, but few inside Turf Moor would have cared about that had it delivered victory in a fixture which had taken on huge importance for both sides.

Luton had more of the ball but it was Burnley that looked more threatening, with Wilson Odobert in particular showing why Vincent Kompany had said the 19-year-old was among a group of players whose emergence persuaded him to pull a contract offer to Andros Townsend, who instead started for Luton.

Burnley had a huge chance seven minutes in when Amdouni’s pass put Gudmundsson through on goal, but former Blackburn Rovers goalkeeper Kaminski got down to make a vital save.

That looked like it might be costly for Burnley as Luton seized control of the game for the next 25 minutes, with Ross Barkley dictating play and going close himself with a curling shot touched over by Trafford.

Chiedozie Ogbene tested Trafford from a tight angle before playing a low ball in for Albert Sambi Lokonga, who was guilty of scuffing a very presentable chance.

Burnley was struggling to get over the halfway line but Odobert always looked their most likely outlet down the left-hand side.

The teenager cut in from the left and watched a curling shot drift just over in the 35th minute, but then set up the opening goal moments later.

Odobert got past Teden Mengi inside the box and pulled the ball back, with his cross taking a slight deflection to fall for Amdouni to fire at goal, beating Kaminski as Gudmundsson applied pressure.

Burnley made a bright start to the second half and Lyle Foster should have played Amdouni in, instead over-hitting his pass inside the box. Next, Josh Cullen’s pass found Vitinho, who easily turned away from Doughty but sent his left-footed shot over the crossbar.

Odobert was unlucky just after the hour, cutting inside to get away from Ogbene before his shot took a wicked deflection off Mengi, forcing Kaminski to scramble over and push the ball to safety.

Odobert went close again 10 minutes from time. Substitute Connor Roberts, strongly linked with a January move to Leeds, took a free-kick quickly to set Odobert away down the right and he darted towards goal before stinging the palms of Kaminski.

But just as Burnley fans prepared to celebrate, the mood changed in stoppage-time. Trafford had comfortably collected everything Luton had thrown at him late in the game and should have had Doughty’s cross under control.

But Adebayo blocked his path and that left an open goal for Morris to score his fourth of the season.