Sidelined since mid-September by a hamstring injury, France midfielder Pogba made a decisive return as Jose Mourinho's side restored the eight-point gap that separates them from Premier League leaders City.
Pep Guardiola's City had earlier prevailed 2-0 at Leicester City and there were also wins for champions Chelsea, Liverpool and Arsenal, who beat Tottenham Hotspur 2-0 in the north London derby.
"We can only play Manchester City twice in a season," United manager Mourinho told BT Sport.
United remain second, a point above Chelsea, who climbed above Tottenham into third place courtesy of a 4-0 success at West Bromwich Albion.
More From This Section
In addition to Pogba, Zlatan Ibrahimovic received a rapturous reception from United's fans when he came on as a substitute following his recovery from a serious knee injury.
"The return of the injured players was nice, especially in Zlatan's case, after such a dramatic injury," said Mourinho. "To see him back was a great emotion."
A slip by Victor Lindelof enabled Dwight Gayle to put Newcastle ahead in the 14th minute with the first league goal United had conceded at Old Trafford since April.
Romelu Lukaku added a fourth, swapping passes with Juan Mata and thrashing home to end a seven-game goal drought.
At Leicester, Gabriel Jesus and Kevin De Bruyne struck fine goals as ruthless Manchester City registered a 16th successive victory in all competitions.
Jesus finished off a slick move shortly before half-time and De Bruyne made it 2-0 early in the second half with a blistering left-foot shot into the top-left corner.
"We continue with our good rhythm in terms of points and the way we play."
- Salah top scorer -
====================
City captain Vincent Kompany made his first league start since August following his latest calf injury.
But in a major blow for the visitors, Guardiola said fellow centre-back John Stones was facing "four to six weeks" out after being forced off in the first half with a hamstring problem.
Chelsea piled the pressure on West Brom manager Tony Pulis with a breezy 4-0 win at The Hawthorns, where Antonio Conte's side secured the title last season.
Quick-fire first-half goals by Shkodran Mustafi and Alexis Sanchez earned Arsenal a richly deserved victory over arch rivals Tottenham at the Emirates Stadium.
"They had the urgency, the desire and the focus," Arsenal manager Arsene Wenger said of his players.
"In a derby like that, that plays a part. We didn't lose the defensive focus for 90 minutes."
Spurs manager Mauricio Pochettino felt, with justification, that the free-kick that led to Mustafi's goal should not have been awarded and that Mustafi had been offside from Mesut Ozil's cross.
Liverpool remain fifth, above sixth-place Arsenal on goal difference, after a routine 3-0 home win over Southampton at Anfield.
Egyptian forward Mohamed Salah scored two first-half goals -- the first a magnificent curler -- to become the Premier League's leading scorer on nine goals, with Philippe Coutinho adding a third.
High-flying Burnley also sit on 22 points after Jack Cork and Ashley Barnes scored in a 2-0 home win over second-bottom Swansea City.
Bottom club Crystal Palace were twice pegged back in a lively 2-2 home draw with Everton, for whom David Unsworth remains in charge on a caretaker basis.
Callum Wilson netted a hat-trick and Harry Arter also found the net as Bournemouth belied the dismissal of defender Simon Francis to beat Huddersfield Town 4-0 and move clear of the relegation zone.