Steve Bruce's side took the lead inside 120 seconds through Luke Shaw's own goal, courtesy of Emil Krafth's teasing cross, before Harry Maguire's first-half header levelled the Premier League clash.
Despite United goalkeeper Karl Darlow saving Bruno Fernandes' second-half penalty, it was late agony for the hosts as the Portuguese midfielder gave the Red Devils the lead before further strikes from Aaron Wan-Bissaka and Marcus Rashford sealed Newcastle's defeat.
The Magpies headed into the top-flight clash searching for back-to-back Premier League victories for the first time since June and faced a Manchester United side who had suffered a humiliating 6-1 home defeat to Tottenham Hotspur in their recent Premier League outing.
And it was Newcastle who got off to a perfect start after breaking the deadlock through Shaw's misfortune inside the opening two minutes. After neat build-up play, consisting of Allan Saint-Maximin and Jonjo Shelvey, the latter played a forward pass to Krafth before the Swede's dangerous cross was deflected into his own net by the English left-back.
Fernandes looked to have restored parity for the Red Devils after linking up with Juan Mata before tucking the ball into the top corner. However, VAR ruled out the goal due to Mata straying into an offside position.
In the 23rd minute, Ole Gunnar Solskjær's men levelled the encounter through Maguire. After Darlow had initially pushed away Mata's drive, the resulting corner from the Spaniard was met by by the Red Devils captain and directed into the far corner.
Saint-Maximin, who signed a new six-year deal with United earlier this week, almost regained the Magpies' lead in terrific fashion as the Frenchman's ferocious 25-yard effort was brilliantly kept out by David de Gea.
Darlow was on hand to prevent United falling behind before the break with a number of important stops, firstly tipping Aaron Wan-Bissaka's cross-cum shot away for a corner before beating Marcus Rashford's low drive from the edge of the box before the half-time whistle.
Shortly after the restart, Isaac Hayden was withdrawn due to a hamstring injury before Callum Wilson went agonisingly close to netting his fifth league goal in as many games as the forward got onto the end of Saint-Maximin's teasing cross before seeing his flick towards goal clawed off the line by the stretching De Gea.
Newcastle conceded a penalty in the 56th minute as Rashford went down in the box after Jamal Lewis was adjudged to foul the England international, with referee Craig Pawson consulting the pitch-side monitor before awarding the spot-kick.
Fernandes, who had previously netted ten consecutive penalties in all competitions since joining the club in January, was unable to convert from 12 yards as Darlow guessed the correct way to palm away the fierce attempt.
From the resulting corner, Shelvey cleared Maguire's header off the line before taking his turn in front of goal as the 28-year-old's stinging effort from 20 yards was pushed away by De Gea.
With full-time approaching, Newcastle were dealt a devastating blow as the Red Devils took the lead in the 86th minute. After a dangerous counter-attacking move, Rashford teed up Fernandes inside the penalty area, who curled the ball into the top right-hand corner.
The Magpies fell further behind in the 90th minute through Wan-Bissaka as the full-back advanced into the penalty area before unleashing a powerful effort into the roof of the net, his first goal for the club.
Rashford then completed the scoring in the dying moments of the contest after racing onto Fernandes' lofted through ball before calmly finishing past Darlow.
Newcastle United: Karl Darlow, Emil Krafth, Jamaal Lascelles (c), Federico Fernández, Jamal Lewis, Isaac Hayden (Fabian Schär 49), Jonjo Shelvey, Jeff Hendrick (Miguel Almirón 88), Joelinton (Ryan Fraser 72), Allan Saint-Maximin, Callum Wilson.
Subs not used: Mark Gillespie, Javier Manquillo, Jacob Murphy, Andy Carroll.
