Raheem Sterling headed in the opener for Pep Guardiola's charges before Aymeric Laporte turned home a second from close range after Martin Dúbravka had parried Ilkay Gundogan's volley.
Rodri nodded in a simple third after the break before further efforts from Phil Foden, who swept home after a swift breakaway, and Sterling, who sidefooted in with aplomb in the dying moments, completed the scoring on a miserable afternoon for Newcastle.
The only positive for the visitors was the return of Callum Wilson and Kieran Trippier from injury, with the pair making their comebacks towards the end of the game at the Etihad Stadium.
Somewhat predictably, this term's champions-elect set the pace, with the faultless Kevin De Bruyne at the heart of most of their best moves. After the Belgian sent a free kick wide, though, United wasted a glorious opportunity to open the scoring when Allan Saint-Maximin's cross was met by Chris Wood at the back post. Both he and Joelinton were unmarked but the New Zealander met it first, heading down into the ground and straight at Ederson.
There were two further warnings for the Magpies before they went behind. Laporte blazed over after De Bruyne picked him out with a corner and then the same man crossed for Joao Cancelo, who somehow miscued on the half volley with the goal at his mercy.
In the end, Cancelo didn’t have to wait long for one of his dangerous forward bursts to bear fruit. It was the Portuguese full back who stole in behind Saint-Maximin to nod Gundogan's clipped pass back across goal, where Sterling was waiting to head it home with 19 minutes gone.
Eddie Howe's side thought they had levelled soon after when Jamaal Lascelles met Matt Targett’s corner, heading it straight at Bruno Guimarães. The ball fell fortuitously for Wood to prod home, but his effort was disallowed because of Guimarães' inadvertent touch while in an offside position.
City continued to create openings with almost metronomic regularity, with Cancelo forcing a smart save from Dúbravka and Oleksandr Zinchenko firing across the six-yard box to no avail. Seven minutes before the break, they made it two when De Bruyne found Gundogan on the edge of the box from a corner. The German caught his volley well but Dúbravka was only able to parry it, and after Ruben Dias had had a stab at the rebound, Laporte made sure from close range.
Guardiola’s men began the second period in a similarly dominant manner, with Gabriel Jesus turning in the box and almost managing to square for De Bruyne to roll it in. Veteran midfielder Fernandinho was introduced to play centre half alongside Laporte and though the change didn’t disrupt the hosts' rhythm, there were a few fleeting moments of promise for United in the final third; Guimarães fired one over the bar before Saint-Maximin, cutting in from the left, pulled his shot wide of the upright in front of the travelling supporters.
Any lingering hopes of a comeback were dashed just after the hour, though, as De Bruyne created a third for his side. It came from another corner, swung in by the former Chelsea man straight onto the head of Rodri, who shrugged off Emil Krafth and planted his header beyond Dúbravka at the near post.
Dúbravka then pulled off a terrific save to tip Zinchenko’s drive over the bar and deny City a fourth before Wilson and Trippier made their returns, with both players coming off the bench with a quarter of the contest remaining. Wilson, out since December, and Trippier, who had been injured since February, lifted United momentarily in what was a slog of a second half. United's best chance of the final ten minutes actually fell to Wilson; fellow substitute Jacob Murphy played him in but Ederson foiled him as he tried to slot home.
It would have proved to be merely a consolation. Foden's swept finish after Zinchenko's miscue in added time gave City a fourth before Sterling thumped home his second of the contest to add extra gloss to the scoreline and round off a day to forget for United, who face Arsenal in their final home game of the campaign a week on Monday.
