Brave Burnley secured their first away point of the season with a magnificent rearguard action led by returning hero Tom Heaton.
Heaton produced a goalkeeping masterclass to keep his former club at bay as the Clarets avoided defeat at Old Trafford for the first time since 1974.
Burnley's last win at Manchester United came in 1962 and while the wait goes on to re-write that bit of history, this performance will be remembered for a long time by the Clarets' supporters who filled their corner of the famous old ground.
Burnley defended magnificently and competed superbly with United - down to 10 men for the last 25 minutes following the dismissal of Ander Herrera and with Jose Mourinho watching from the directors' box after his own half-time dismissal - simply unable to overcome a display full of commitment and character that epitomised everything Sean Dyche has brought to Burnley on the eve of his fourth anniversary as manager.
United had won just one of their previous six league games but knocked Manchester City out of the EFL Cup in mid-week to steady the ship.
Manager Mourinho stuck with nine of that starting line-up as Wayne Rooney's return got only as far as a place among the substitutes.
Zlatan Ibrahimovic therefore continued to lead the home's side attack, with support from Marcus Rashford and Jesse Lingard in the wide positions, but the big summer signing had gone five consecutive league games without scoring for the first time since 2010.
And the former Paris St-Germain, Barcelona and Inter Milan striker was kept waiting when Heaton made the first of a handful of top-class saves which added up to an afternoon of torment for the Swedish star.
Ibrahimovic and captain Juan Mata looked to combine at every opportunity and when Mata slipped in Ibrahimovic in, the 35-year-old looked a certain scorer until Heaton spread himself to make a fine block.
Ibrahimovic then returned the favour for Mata to test Heaton with a shot low to the keeper's right.
But Heaton, who came through the ranks at United to launch his career, was determined not to be beaten and went on to make another couple of fine saves before the break, turning a Jesse Lingard header over the bar and touching over a fierce drive from Paul Pogba, the world's most expensive player.
And when Burnley's England man needed help, it was always on hand as the Clarets defended with great discipline, Ben Mee again being in the perfect place to block another goalbound effort from Ibrahmovic following a clever flick from Pogba.
Not that it was all one-way traffic as Burnley grew into the contest and had a couple of openings of their own.
Andre Gray, back in the side following his four-match ban, had an early shot blocked before Michael Keane, another to excel on his return to Old Trafford, headed wide from a corner and shot at David de Gea.
But if the first half was exciting, it was nothing compared to the drama of the second as United threw everything at the Clarets in an effort to force a breakthrough.
Yet again, though, Dyche's men refused to buckle with Heaton an inspired figure behind a wall of blue shirts which noew featured Jon Flanagan at left-back in place of the injured Stephen Ward.
Mata and Ibrahimovic used all their class to try and find a way through but both were again thwarted by Heaton, the save from the Clarets' captain to keep out a close-range effort from Ibrahimovic typical of Peter Schmeichel - one of Heaton's heroes - at the former United keeper's best.
Both United players then hit the woodwork, Ibrahimovic with the aid of a deflection off Jeff Hendrick, before the home side was reduced to 10 men when Herrera was sent off for a second booking, unfortunately received when he appeared to lose his footing when sliding into Dean Marney.
United then sent on Rooney and Marouane Fellaini but, with an extra man, Burnley sensed the possibility of a goal of their own.
They had already had a couple of chances with Gray not being able to give Luke Shaw the slip on the break and Scott Arfield shooting over before Ashley Barnes glanced a header just wide from Johann Berg Gudmundsson's cross after coming off the bench for his first appearance of the season.
But despite enjoying more possession, the Clarets couldn't force a clear-cut opening and it was United who nearly grabbed a dramatic late winner with one last chance for Ibrahimovic which he stabbed wide and a mis-cued effort from Rooney in stoppage time before Burnley could celebrate a landmark result in their top-flight return.
Burnley: Heaton, Lowton, Keane, Mee, Ward (Flanagan 44), Gudmundsson (Boyd 85), Marney, Hendrick, Arfield, Gray (Barnes 59), Vokes. Substitutes: Robinson, Kightly, Bamford, Tarkowski.
Manchester United: De Gea; Darmian, Rojo, Blind, Shaw, Herrera, Mata (Fellaini 73), Rashford (Memphis 82), Pogba, Lingard (Rooney 73), Ibrahimovic. Substitutes: Romero, Carrick, Schneiderlin, Young.