A lacklustre first half came to life in the 39th minute when Mata curled an exquisite free-kick past Rob Elliot and into the top corner, and the Spaniard then showed great composure to make it 2-0 five minutes into the second half after being found in the box by Javier Hernandez.
Hernandez added a third with a predatory finish from Shinji Kagawa's pass and Mata provided another moment of magic to set up the fourth as a clever back-heel allowed Adnan Januzaj to fire home and complete the rout.
Anders Lindegaard did have to pull off a couple of superb stops to deny Papiss Cisse but Newcastle were disappointing throughout and boos rang out around St James' Park at the final whistle.
There was an end-of-season feel about the game before kick-off, with David Moyes keeping one eye on Munich as he made eight changes and opposite number Alan Pardew missing five of the men who started the 1-0 win at Old Trafford in December.
As a result, there was inevitably a makeshift look about both sides with United patient in their build-up, in which a deep-sitting Marouane Fellaini figured prominently, as they tried to find space for Hernandez and Mata.
Newcastle's approach was more direct with Davide Santon, lining up at right-back rather than on the left, making life difficult for Patrice Evra to supply a series of dangerous crosses.
It was he who produced the second-minute ball from which Dan Gosling, making his first Barclays Premier League start for the Magpies since December 2011, headed just wide, and he who picked out striker Cisse to force a fine 24th-minute save from Anders Lindegaard with a glancing header.
But, too often, the home side squandered possession in promising positions to let the visitors off the hook.
Moyes' men, who lost winger Ashley Young with a dislocated finger after just 18 minutes, were little more threatening with keeper Elliot having little to do for much of the first half.
However, the game turned six minutes before the break and it did so in controversial circumstances.
Gosling was furious to be penalised for a trip on Darren Fletcher on the edge of the box, but as the home fans made their feelings known to referee Kevin Friend, Mata stepped up to curl a delicious left-foot free-kick high into the top corner with Elliot powerless to resist.
The game could have been effectively over in the final minute of the half when, after Friend had allowed play to continue with central defender Mike Williamson appealing for a foul by Hernandez, the Mexican ran on to Kagawa's through-ball to shoot past Elliot, only to see the ball come back off the foot of the post.
However, any hopes of a fightback were dealt a fatal blow within five minutes of the restart and this time Newcastle had no-one to blame but themselves.
Skipper Fabricio Coloccini's ambitious attempt to chest a long ball to full-back Massadio Haidara fell short and Kagawa stole in to pick out Hernandez's run.
The striker fed Mata inside the box and he cleverly side-stepped Coloccini's desperate lunge before slotting calmly into the bottom corner.
Hernandez might have made it 3-0 with a snapshot which flew over on the hour, and it was then that the Magpies opted for change with Hatem Ben Arfa replacing the ineffectual Luuk De Jong.
But Hernandez made amends with 25 minutes remaining when he slid home from close range after Januzaj and Kagawa teamed up to play him in.
Lindegaard had to turn away Cisse's curling 71st-minute effort and then produced a remarkable stop to deny the same man from just six yards before Mata set up Januzaj to complete the rout with an audacious back-heeled pass.