An injury-time strike from Manchester United's Jess Lingard ensured that the spoils were shared at Old Trafford as it had looked like a major upset was on as Burnley's incredible season of results continued.
Both sides came into the fixture in decent, rather than spectacular, form. Jose Mourinho's Reds had won four of their last six league games but were still a distant second behind runaway league leaders Manchester City.
Burnley, who have had a terrific season so far, were 7th and only two points outside the Champions League places. They had only lost two of their last six games, although their last match had seen Tottenham Hotspur dispose of the Clarets 3-0 at Turf Moor.
Mourinho made four changes to the United side that disappointingly drew against Leicester City with Marcos Rojo, Luke Shaw, Marcus Rashford and Zlatan Ibrahimovic all starting in a 4-4-2 formation. For Sean Dyche he kept to his tried and tested personnel with one enforced change for Burnley being Ashley Barnes replacing the injured Chris Wood in attack in a slightly more defensive 4-5-1 formation.
To the surprise of the boisterous home crowd, Burnley started brightly and earned a free kick after a foul by Marcos Rojo on Jeff Hendrick within the first few minutes. A terrifically flighted ball by Johann Brag Gudmundsson into the United penalty area was clinically fired home by the recalled Ashley Barnes after United were unable to clear the first header.
The early goal sparked United into life and they began to impose themselves, but Burnley remained undaunted. Gudmundsson was causing the hosts problems and delivered yet another quality ball into the penalty area that Scott Arfield deftly volleyed on to United's bar, which left David De Gea in United's goal stranded, but it sympathetically bounced away for a goal kick.
United were picking up the pace and created a few opportunities in a short space of time; Juan Mata had a shot blocked, RomeluLukaku almost got on the end of an Ashley Young cross and then Young himself brought a first save of the match from Nick Pope with a rasping shot from 25 yards out - but the Clarets remained unbreached.
Sustained pressure continued from United with Paul Pogba dictating in midfield, a couple of free-kicks punched clear by Nick Pope, followed by a flurry of corners. Burnley showed their dogged resistance which has served them so well this season, although they remained a threat on the counter-attack.
Burnley extended their lead in the 35th minute after earning a free kick on the edge of the Reds' area, 25 yards from goal. Belgium international Steven Defour stepped up and sublimely curled the ball over the wall and into the top corner, past De Gea's despairing dive. Temporarily, Old Trafford descended into a deafening silence.
The half drew to a close with United pressing, but Dyche's side worked tirelessly to maintain their priceless lead.
United tactically reshuffled for the start of the second half as NemanjaMatic started at center back partnering Phil Jones as Rojo and Ibrahimovic were replaced by Jesse Lingard and HenrikhMkhitaryan, but the Reds continued to press.
A wonderful Ashley Young cross along the six-yard line was guided purposefully towards goal by Jesse Lingard, which Pope did magnificently to deflect on to the crossbar and away to safety.
Within minutes, United hauled themselves back into the match as Young crossed again and Lingard cleverly backheeled into the corner of the net which sent the Theatre of Dreams into an eruption of noise.
United continued to work both flanks well with Shaw and Young looking threatening. The Reds were encamped in Burnley's half, but the Clarets had numbers back to repel the waves of attack as they peppered Pope's goal.
United had a free kick in a similar position to Defour's in the first half after Bardsley had lunged at Mkhitaryan. Pogba stepped up and went for the same corner of the goal too, but his effort was slightly too high and flew disappointingly into the Stretford End rather than the net.
As the game wore on, United seemed to run out of ideas and their approach became more direct than using the subtle play they had adopted earlier, to try to break down the resistance of the Burnley's defensive rearguard. Ultimately, the pressure told as a late free-kick from Juan Mata in stoppage time was converted by Lingard on the half-volley for United's equalizer and the England international's second of the match.
For all United's possession and continued pressing it is hard to begrudge Dyche's men at least the draw as they tenaciously got through many challenging spells during an enthralling contest.