Taking advantage of some poor defending by the hosts, Sean Dyche’s men raced into a 1-0 lead when Ashley Barnes scored from close-range in the 2nd minute.
Jose Mourinho started Zlatan Ibrahimovic and Romelu Lukaku together for the first time this season, but the two big forwards weren’t looking like they were forming a deadly strike partnership as the Red Devils looked extremely sluggish in attack.
Steven Defour would score a masterful free-kick late in the first-half to compound United’s misery and somehow, the Clarets hung on to their 2-0 lead till the interval.
Mourinho knew he needed to make drastic changes if his side were to come back in the tie and the Portuguese tactician responded by taking off the disappointing duo of Marcos Rojo and Zlatan Ibrahimovic in favour for Henrikh Mkhitaryan and Jesse Lingard.
And the latter would be United’s saviour, reducing the deficit with a deft flick in the 53rd minute, just moments after missing a gilt-edged chance.
With the early goal in the second-half, United had their tails up and buoyed by the home support, bombarded the Burnley box with a deluge of crosses.
Ashley Young, Luke Shaw, Marcus Rashford and Juan Mata were among the thing of things, trying to find a way to get the ball on Lukaku’s head, but as the clock ticked, the Red Devils started to get more desperate.
Burnley were content by defending deep and seemed to have held on for their first win at Old Trafford in over half a century, but Lingard popped up with an equaliser deep in injury time to prevent United from falling to a second home defeat of the season.
While Burnley will feel that a draw was unjust after their brilliant first-half, the second period was all United and both sides will go home disappointed with the result.
For United it’s the second 2-2 draw in as many matches, a game in which their defensive frailties were exposed once again and with league leaders travelling to Newcastle United on Wednesday, the gap at the top of the Premier League summit could widen to an gargantuan 15 points.
To make matters worse for Mourinho, his former club Chelsea beat Brighton and Hove Albion 2-0 to close within a point of the Red Devils.
Burnley may be winless in their past three games, but they will depart Old Trafford with their heads held high and an invaluable point earned.
The Clarets travel to Premier League newcomers Huddersfield Town on Saturday for their next game, while United host Southampton on the same day.