The dismal hosts - easily beaten in a one-sided Manchester derby by rivals City on Sunday - were brushed aside again at Old Trafford by a confident Toon side who exacted revenge for last season's painful Carabao Cup final defeat in Wednesday's fourth-round tie, sealing their spot in this year's quarter-finals in the process.
Miguel Almiron - an early replacement for the injured Matt Targett - started the party for much-changed Newcastle shortly before the half-hour mark, catching Diogo Dalot sleeping and blasting beyond Andre Onana on the stretch after man-of-the-match Tino Livramento had dispossessed Alejandro Garnacho and breezed past Mason Mount and Hannibal Mejbri all too easily.
Just eight minutes later the lead was doubled, Chelsea loanee Lewis Hall dispatching a perfect left-footed volley into the bottom corner of the net after Harry Maguire met Joe Willock's cross with a weak clearing header following a great scooped pass from Almiron to trick the under-par Dalot.
Loud boos greeted the half-time whistle as the jubilant 7,000 away fans aimed loud chants of 'you're getting sacked in the morning' at Ten Hag, who sent on the fit-again Aaron Wan-Bissaka and Sofyan Amrabat at the break.
That double switch looked to be working as his team made a purposeful and energetic start to the second half, but Newcastle still looked dangerous on the counter-attack and hopes of a comeback were firmly extinguished on the hour when Amrabat was tackled by Joelinton and Willock thrust to the edge of the box, with Maguire and Victor Lindelof distracted by the run of Anthony Gordon as the former Arsenal midfielder coolly slotted into the bottom corner.
Ten Hag - who made seven changes from the derby to Eddie Howe's eight as both managers heavily rotated their starting lineups on Wednesday - introduced the likes of Marcus Rashford, Rasmus Hojlund and Bruno Fernandes in a vain attempt to salvage some pride from another chastening night in front of their own fans, many of whom understandably flooded to the exits early again.
But there was nothing to bother their former loanee Martin Dubravka in the closing stages, with Newcastle looking the mostly likely to further extend their advantage as Sean Longstaff - stand-in captain on his 150th Magpies outing - whistled a brilliant effort narrowly beyond the far post.
Fernandes wasted United's best chance of the night at the front post after a fine slipped pass from Antony, while Onana denied Emil Krafth - making his first Newcastle appearance since suffering a serious knee injury in this competition against Tranmere last August - and Lindelof blocked from Callum Wilson.
Only a second away win over United in 42 attempts spanning 51 years was the perfect tonic for Newcastle after mounting fitness issues and the distraction of Sandro Tonali's 10-month betting ban had led to a run of just one win in four matches since their famous thrashing of Paris Saint-Germain in the Champions League last month.
They host title-chasing Arsenal in a huge Premier League contest next at St James' Park on Saturday, while Ten Hag will have to figure things out fast ahead of a potentially tricky lunchtime trip to Fulham.