The Red Devils went into the Premier League's only Boxing Day fixture without a home win in two months and missing seven first-team players, including talisman Bruno Fernandes.
But Ruben Amorim's rejigged side rallied as they started with a back four and dug deep at the end to secure a 1-0 triumph courtesy of Dorgu's delightful volley as the wing-back impressed on the right wing.
It was an impressive all-action display by the versatile Denmark international, whose manager last month admitted he could "feel the anxiety" every time he touched the ball.
There were no such concerns on Friday evening as Dorgu followed his first-half strike with some impressive defensive contributions as United kept just their second clean sheet of the season.
Lewis Hall struck the crossbar as Newcastle pushed strongly for a leveller, with Eddie Howe's side tasting more disappointment on the road.
United reverted to a back five for the closing stages of a match that began with Lisandro Martinez in a central defensive two and wearing the captain's armband as he made his first start in 327 days.
The hosts' other alteration Casemiro went close with an early header and Newcastle initially struggled to get to grips with Amorim's altered approach.
Benjamin Sesko should have done better than balloon wide on the turn after fine work by Dorgu, but the Magpies would settle.
Senne Lammens had to be alert to stop Bruno Guimaraes' near-post nod from a corner, with the hosts having to swat away other half-chances during a dicey spell.
Amorim's men held firm and a smart Sesko flick to Matheus Cunha helped swing the game in their favour, with Aaron Ramsdale beating away the Brazilian's drive before the ball was hacked out of play.
Diogo Dalot sent over the resulting throw-in and Nick Woltemade's headed clearance looped high, with Dorgu racing onto the ball hitting a crisp volley that flew home.
Ramsdale got a hand to the strike but could not stop it from finding the net, although Newcastle's goalkeeper would prevent him from a threatening cross-shot and then a low strike.
Cunha lasered wide of the near post before a half-time break that Mason Mount did not return from. Jack Fletcher, son of United favourite Darren, came on for his home debut.
Newcastle were in control and bossing possession, only for Guimaraes to be robbed and Sesko to be put in to rifle off the crossbar.
The striker was brought off straight after, along with a surprised Casemiro, and the woodwork was soon rattled at the other end as Hall's dipping effort from distance that beat Lammens came off the bar.
Hall looked a threat and Newcastle hoped to be awarded a penalty for handball against Martinez from a Schar strike, but the VAR decided against it after a lengthy review.
Anthony Gordon hit a low strike across the face of goal and Newcastle continued to knock at the door.
Amorim's side were penned back as Newcastle attempted to find a gap, with balls defended strongly and Lewis Miley slamming wide as the match entered stoppage time.
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