A late rush of blood from Manchester United goalkeeper Andre Onana threw Burnley a relegation lifeline at Old Trafford.
United were on the verge of taking the points when Antony took advantage of a Sander Berge error to give the home side the lead after 80 minutes.
But Onana – who had made a series of saves earlier in the afternoon – erased his notebook by charging into Zeki Amdouni as he came in front of a cross.
Referee John Brook was advised by VAR to check his monitor and Amdouni made no mistake from the spot with just three minutes of normal time remaining.
The result left United in sixth place as Vincent Kompany’s side moved within two points of safety as Nottingham Forest faced Manchester City on Sunday.
Antony celebrates his goal to give Manchester United a late lead against Burnley
The Brazilian gave United a late lead that they could not hold in a 43-shot match
Antony receives a hug from Alejandro Garnacho as the Old Trafford crowd celebrates his goal
In an entertaining match that saw 43 shots, the only surprise was that there weren’t more goals, with Bruno Fernandes hitting the woodwork for United and Onana twice making brilliant saves to deny Lyle Foster.
For Erik ten Hag there was also the embarrassment of being booed by his own fans when he decided to take Kobbie Mainoo off the field halfway through the second half.
Despite Burnley’s lowly position in the league, they arrived at Old Trafford in slightly better form than their hosts.
Vincent Kompany’s side had taken ten points from their previous seven games, compared to United’s nine.
A remarkably open start saw David Fofana find United’s centre-back Casemiro’s target after just 19 seconds, but shoot straight at Onana.
United went straight to the other end, with Alejandro Garnacho firing over from eight yards.
Antony then tried his luck from 25 yards and Cristian Eriksen curled wide as the home pressure grew.
Antony, who has had a disappointing season following allegations about his private life, looked in the mood to shine. The winger played one outrageous pass with his back and then tested Muric with a low drive.
Andre Onana handed Burnley a relegation lifeline when he crashed into Zeki Amdouni
Onana’s challenge earned Burnley a late penalty, which they took advantage of to take a point
Amdouni celebrates after scoring the penalty, earning the Clarets a valuable point
When Burnley almost imploded on itself by offering Christian Eriksen the ball halfway through their own half, the Dane let go. Bruno Fernandes was stopped by a beautiful block from Maxime Esteve.
Fernandes also grabbed the crossbar after a good raid from Rasmus Hojlund as United knocked on the door.
Not that Burnley didn’t also carry their own threat. On 27 minutes, Wilson Odobert’s curler from outside the box forced Onana into an acrobatic tip-over.
United’s famously weak defense then gave up another chance in the penalty area to Foster, who couldn’t get his feet in order and stuck it wide.
Antony is denied from close range by Burnley goalkeeper Arijanet Muric in the second half
Casemiro goes to the ground under pressure from David Datro Fofana as United go forward
Andre Onana makes a save to maintain parity for Manchester United in the opening 45
Vincent Kompany stood tall on a technical level and urged encouragement. A save from Onana was needed to keep the score level after 35 minutes.
Josh Cullen set up Foster, whose header headed towards the top corner before Onana reached the ball with a great leap and tipped it around the post.
It was the same game again when Sander Berge slid into Foster. The attacker only had Onana to beat, but the big Cameroonian stopper reduced the angle and smothered his shot.
A goalless first half was not what Olympic superstar and United diehard Usain Bolt would have wanted to see during his visit to Old Trafford.
He was probably wondering if Marcus Rashford could have made an impact. The struggling England forward was absent again after being punched during last weekend’s FA Cup semi-final after posting a late-night social media message to defend himself from online abuse.
Manchester United players try to block a free kick from Burnley’s Jacob Bruun Larsen
Frustration among United trio Christian Eriksen, Casemiro and Antony during the opening half
United started the second half energetically. Garnacho pushed his way past Lorenz Assignon, but his cuts prevented Antony from converting. The Brazilian then had a shot parried by Muric, who spread out to prevent Rasmus Hojlund from taking advantage of the rebound.
Garnacho then opted to shoot at goal when released by Fernandes, while Hojlund waited in the penalty area for a cross that never came.
When Hojlund then approached Aaron wan-Bissaka instead of shooting himself, the defender waited too long for the ball to reach him and the opportunity was lost.
Ten Hag’s double substitution midway through the second half caused boos around Old Trafford as Mainoo’s number 37 was put on the board. He and Hojlund left with Scott McTominay and Amad Diallo in their place.
The response was almost immediate, with Garnacho catching half a volley, just right, for Muric to turn away.
Onana makes a block to deny Burnley’s Lyle Foster after receiving the goal-side clearance from Harry Maguire
Christian Eriksen takes aim at the Clarets goal during the first half at Old Trafford
Burnley’s David Datro Fofana outpaces Casemiro as Burnley look to mount an attack
United’s only fit senior centre-back Harry Maguire underlined his value with a superb block to deny Lorenz Assignon after Cullen and Berge had sliced open the home defence.
The deadlock was finally broken when Berge’s crossfield pass was intercepted in his own half by the alert Antony.
He then sprinted away to beat Muric and looked emotional as he scored, burying his head on Fernandes’ shoulder, pushing the ball under his shirt and flashing a hug to mark his girlfriend’s pregnancy.
Burnley refused to throw in the towel and had Onana to thank for an equalizer. He came out to receive a cross and ran into Amdouni as he missed.
United striker Rasmus Hojlund takes on Burnley’s Jacob Bruun Larsen during the match
United’s Brazilian winger Antony is surrounded by three Burnley players
The Cameroon international got away with a similar challenge against Wolves on the opening weekend of the season, but not this time.
Amdouni scored the penalty and Burnley are still hopeful as they extended their run to one defeat in eight.