Mata curled in a sublime free-kick on 39 minutes to break the deadlock and added a second from close range five minutes after the break following good work from Javier Hernandez.
Newcastle never looked like mounting a comeback and Hernandez celebrated a rare start by adding a third on 64 minutes before Adnan Januzaj struck late on.
|VIEW FROM ST JAMES' PARK
|By Harry Slavin
Manchester United have followed up their impressive display against Bayern with another terrific display, but this one was all down to one man.
Juan Mata, starting from a central position, controlled the game from start to finish, peppering the game with sublime touches and measured passes which culminated in two fine goals and one audacious assist.
Newcastle on the other hand have well and truly given up the ghost for the season. The sooner they put this campaign to bed the better, as the damaging results keep racking up. That’s now 11 goals in just three games Alan Pardew’s side have conceded.
Yet Moyes, who was without the injured Wayne Rooney and Robin van Persie, will take his charges to Munich high on confidence as United seek to follow up last week's 1-1 draw with Bayern by progressing to the last four of Europe's premier club competition.
Ashley Young and Hernandez linked up twice in quick succession early on to force Mike Williamson into carbon-copy near-post clearances, before Marouane Fellaini was penalised for handball when trying to control and shoot inside the box.
Winger Young was forced off the field for treatment on a hand injury with 14 minutes on the clock and Newcastle looked to capitalise as Cheick Tiote flashed a powerful effort over the bar from 15 yards.
The injury ultimately brought a premature end to Young's afternoon, with Januzaj introduced in his place.
An ambitious overheard kick from Papiss Cisse proved simple for Anders Lindegaard to gather as the Dane settled into his first top-flight game since the 5-5 draw at West Brom on the final day of last season.
The stand-in goalkeeper was called into action again midway through the half, tipping Cisse's powerful header over the bar.
Opposite number Rob Elliot was less convincing when he came out to punch away a free-kick from Mata, with the close attention of Chris Smalling causing the ball to fall loose for Shinji Kagawa, who could only drag his shot wide.
However, there was nothing Elliot could do to keep out Mata's superb set-piece effort six minutes before the break as the Spain international lifted a curling effort into the top-right corner from the edge of the box for his second goal in as many league games.
The lead could have been doubled on the stroke of half-time but Hernandez struck Elliot's left-hand post with a low shot after racing clear.
Undeterred by that near miss, the away side did extend their advantage just five minutes into the second half, Mata collecting Hernandez's pass before wrong-footing Fabricio Coloccini and Elliot to stroke home.
The impressive Hernandez gave his side breathing space with a close-range finish from Kagawa's 65th-minute cut-back, the Mexican's fourth top-flight goal of the season.
Cisse forced two excellent late saves from Lindegaard but Januzaj added a fourth for the visitors after an excellent one-two with Mata, handing United a measure of revenge for December's 1-0 loss in the reverse fixture.