Reports suggested that United boss Jose Mourinho was just one poor result away from the sack following a miserly run of form, and it looked as though Newcastle would pile even more pressure on the Portuguese manager's shoulders when they took a two-goal lead inside the opening 10 minutes.
It took a stunned United until the final 20 minutes to react, but ultimately Mourinho's changes swung the game in the home side's favour with first-half sub Juan Mata providing the catalyst for a remarkable comeback.
Anthony Martial levelled things up for the hosts six minutes later, and Alexis Sanchez - left out initially but brought on as United's third sub - sealed three crucial points in the final minute of normal time and eased some of the considerable pressure on Mourinho.
Newcastle had not been ahead at any stage of their opening seven Premier League games and had failed to score more than one goal in that time either, but they made a remarkable start to the match to leave United shell-shocked.
The hosts only had themselves to blame for some shoddy defending, though, with Newcastle slicing the defence open far too easily for their first goal when Kenedy latched on to a through-ball, beat Ashley Young and curled his finish past David de Gea into the bottom corner.
The Magpies had registered a league-low 52 shots in their opening seven games, but they had a second goal just three minutes later as Yoshinori Muto piled further misery on the home side.
Once again United were guilty of poor defending, with Muto collecting the ball inside the area with his back to goal and being allowed to turn before thumping his effort past De Gea, who could not react in time.
Remarkably, it was the first time in Premier League history that United had conceded two times inside the opening 10 minutes at Old Trafford, and the hosts suddenly found themselves with a mountain to climb in front of their own fans against a team that had lost five of their previous six games.
It nearly got worse for the 20-time champions of England when Jonjo Shelvey was allowed the space to let fly from range, with his swerving strike almost catching De Gea out.
Mourinho had already seen enough by that stage and made a tactical substitution with less than 20 minutes on the clock as Mata replaced Eric Bailly, forcing Scott McTominay to drop back into an unfamiliar centre-back position.
The decision will raise further questions over the future of Bailly, and it barely improved United's defensive display for the remainder of the first half either as Newcastle continued to look dangerous almost every time they came forward.
United had their moments too, and Nemanja Matic planted one header straight at Martin Dubravka from a corner before Marcus Rashford squandered the hosts' biggest chance of the first half with a header of his own which went wide when he should have scored.
However, despite surrendering the lion's share of possession Newcastle continued to look the most likely to score and it took a fine reaction stop from De Gea to prevent them from effectively killing the game off once and for all, keeping out Muto's close-range header after more lax defending by those in front of him.
Jamaal Lascelles was then left completely unmarked from a free kick but could not make the most of his isolation, and moments later Mohamed Diame drew another save from De Gea after Matic had lost possession inside his own half.
Dubravka was comparatively quiet in the first half, but he did have a save to make shortly before the interval when he got down to keep out Pogba's low effort after a one-two with Lukaku.
There were also decision for referee Anthony Taylor to make at either end of the pitch, with both Young and Muto fortunate to escape being penalised for handballs inside their own penalty areas.
Mourinho had called his defenders' technical ability into question following his side's draw with Valencia in midweek, and he took the opportunity to make a drastic change having seen his side booed off at the break with McTominay being replaced by Marouane Fellaini - leaving United with a back three of Chris Smalling, Matic and Pogba.
It was a decision which invited further scrutiny on his tactics, but one which proved important to United dragging themselves back into the match as they began to play with more rhythm - and a much-needed injection of intensity - from back to front.
The comeback should have begun before the final 20 minutes too, with a low Pogba strike being parried by Dubravka into the path of Matic, who somehow blazed the rebound high and wide of the target with the goal gaping.
Newcastle's own attacking threat had not completely expired, with Matt Ritchie forcing De Gea into a routine save shortly afterwards, but the bulk of the chances were now falling the way of the home side and Mata steered one volley narrowly wide before Rashford squandered another headed opportunity.
The Red Devils still left a lot to be desired defensively and allowed Kenedy into the box too easily shortly before the hour mark, but Mourinho had little choice but to throw caution to the wind and eventual match-winner Sanchez was finally introduced in the 67th minute.
The comeback began just three minutes later, with Martial winning a free kick just outside the area and Mata proceeding to curl the set piece over the wall and into the bottom corner, beyond the despairing dive of Dubravka.
Suddenly Old Trafford began to believe again, although that hope was almost snuffed out immediately when Muto kept the ball alive inside the area and Ritchie flicked an effort goalwards which De Gea thwarted from point-blank range.
It looked as though it might be heroics from Dubravka which would protect Newcastle as United continued to knock on the door, with the keeper making two fine saves to deny Fellaini and then Smalling in the space of just a minute.
Dubravka could not keep out the equaliser moments later, though, as Martial played a smart one-two with Pogba inside the area before whipping his finish past the Newcastle keeper at the near post.
Once again Newcastle responded quickly, and they squandered a glorious chance to regain their lead just two minutes after parity was restored when Diame failed to properly connect with a free header from a corner.
It proved to be a costly miss as the Magpies finally succumbed to the relentless pressure in the final minute of normal time when Sanchez planted a header past the keeper from inside the area for his first goal of the season - and one which may be enough to save Mourinho's job at Old Trafford.
The win takes United up to eighth in the Premier League table, while Newcastle - harshly denied only a second win at Old Trafford since 1972 - are still searching for their first victory of the season and will end the day 19th in the standings.
MAN UTD (4-3-3): De Gea; Young, Bailly (Mata 19'), Smalling, Shaw; McTominay (Fellaini 46'), Matic, Pogba; Rashford (Sanchez 67'), Lukaku, Martial
NEWCASTLE (4-4-1-1): Dubravka; Yedlin, Lascelles, Fernandez, Manquillo; Ritchie, Shelvey, Diame, Kenedy (Murphy 68'); Perez (Joselu 88'); Muto (Atsu 78')body check tags ::