Full-time: Newcastle United 0 Manchester United 4
A goal either side of half-time from Juan Mata put the Premier League champions on course for a tenth away win of the season before Javier Hernandez added a third in the 65th minute.
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David Moyes' men were not finished either, with Mata ending a memorable afternoon with a clever backheel to tee up substitute Adnan Januzaj for the fourth and final goal in stoppage-time.
Those goals meant Newcastle have now conceded 11 in the last three games alone, all ending in defeats without scoring a goal.
Newcastle, sitting safely in the top half of the Premier League table, have now lost ten of their last 15 matches and have failed to score in 11 of those.
Manchester United's stand-in goalkeeper Anders Lindegaard did frustrate the Magpies with three stunning saves to deny Papiss Cisse, but the visitors never looked in any real danger after Mata had opened the scoring with a brilliant 39th minute free-kick.
Newcastle would have been encouraged to see eight changes to the team Moyes sent out in Tuesday's first leg with Bayern Munich in the Champions League quarter-final.
The absence of Wayne Rooney and Robin Van Persie, who remains sidelined with knee trouble, meant an opportunity for Hernandez. The lone Mexican striker struggled to find an opportunity in front of goal initially.
Newcastle created the early openings. Dan Gosling, starting a Premier League game for only the second time since moving to St James' in 2010, had an early header fly wide, while Papiss Cisse turned a tame overhead kick straight at Lindegaard. He also saved from Cisse's thunderbolt with a flying one-handed stop.
But Mata, who scored his first goal for the club against Aston Villa a week earlier, stepped up and curled in a sublime free-kick over the wall and in to goalkeeper Rob Elliot's top left corner in the 39th minute.
Mata added his second soon after the restart. Newcastle captain Fabricio Coloccini chested a long punt from Lindegaard towards Massadio Haidara. Both players left it, Hernandez nipped in and ran at speed deep in to the box.
Hernandez squared and Mata rounded Coloccini before finishing smartly beyond Elliot.
More was to come. When Januzaj, a first half substitute for the injured Young, played Shinji Kagawa through to the byline, the Japan international squared towards the six-yard box.
Hernandez's clever movement got him away from Mike Williamson and he applied the finish beyond Elliot, which merely piled on the frustration for Newcastle's fans.
There were another two fine saves from Lindegaard to deny Cisse but then Januzaj got his name on the scoresheet when he converted following a lovely backheel from Mata.
NEWCASTLE UNITED (4-4-2): Elliot:; Santon, Coloccini, Williamson, Haidara; Anita, Gosling, Tiote, Gouffran (Ameobi 85); De Jong (Ben Arfa 61), Cisse. Subs: Alnwick (gk), Yanga-Mbiwa, Taylor, Dummett, Armstrong.
MANCHESTER UNITED (4-4-2): Lindegaard; Valencia, Smalling, Jones, Evra (Buttner 64); Fletcher, Fellaini (Nani 69); Young 5 (Januzaj 17), Mata, Kagawa; Hernandez. Subs: De Gea (gk), Vidic, Cleverly, Wilson.