The former Frankfurt frontman's scintillating display of finishing put the game beyond Eddie Howe's charges inside the first 33 minutes, with substitute James McAtee's late strike compounding United's misery.
The result leaves Newcastle in seventh place in the Premier League table, three points shy of a place in the top four ahead of next weekend's visit of third-placed Nottingham Forest.
Seeking a first win at the Etihad Stadium since a League Cup triumph under Alan Pardew in 2014 - and a first-ever Premier League victory there - United were buoyed by the return of Anthony Gordon from injury and the inclusion of Dan Burn, who was withdrawn with a groin problem in last weekend's 3-2 Emirates FA Cup win at Birmingham City.
Burn's presence in the back four has tended to bring Newcastle some calm this term, and his timely sliding challenge prevented Erling Haaland from shooting from a tight angle early on, but this was not one of the Newcastle defence's better afternoons; the contest was all but over after 45 minutes. City dominated possession in the opening exchanges, probing for openings, but when the first one arrived Marmoush couldn't keep his shot down.
Before the 20-minute mark, Pep Guardiola's men moved in front in straightforward fashion. Howe will have been frustrating by the manner of Marmoush's first strike, which came from a long ball from goalkeeper Ederson. Kieran Trippier couldn't cut it out and with Martin Dúbravka stranded, the Egyptian forward's lobbed effort bounced into an empty goal.
Five minutes later, Marmoush had his second after picking up İlkay Gündoğan's pass, cutting inside Trippier and firing low beyond Dúbravka at his near post. United's Slovakian stopper then had to save from Savinho, while Burn prevented Phil Foden from tapping in a Haaland cross.
But Marmoush's third, just after the half hour, effectively ended Newcastle's hopes of avoiding an 11th straight defeat at a ground that has proved a thoroughly miserable place to visit over the last two decades. Savinho had enjoyed an impressive first half and it was his cutback that found City's number seven in the middle, and his finish was a simple one.
Lewis Miley and Tino Livramento were introduced at the break in place of Joe Willock and Trippier, and the former's industry in the middle of the park helped shore up the Magpies' midfield initially. Haaland saw a header comfortably held, and after some neat passing at the other end Miley saw a left-footed effort saved by Ederson.
But Howe's men found it difficult to create any clear-cut chances against a rejuvenated City, who jumped back into the top four with this win, which had in truth been confirmed long before McAtee hooked home from close rang with six minutes remaining after latching on to Haaland's front post flick-on from a corner.
United, meanwhile, were able to give striker Callum Wilson some more minutes off the bench as he continues to build his fitness after his return from injury - one of few positives on a day in which the visitors were comprehensively beaten.
