David Moyes made wholesale changes for the trip to Tyneside with only three of the men who started against Bayern Munich in midweek - Phil Jones, Antonio Valencia and Marouane Fellaini - retained with one eye on Wednesday's Champions League quarter-final return leg.
However, once Mata had fired them ahead from a 39th-minute free-kick which Magpies boss Alan Pardew felt should never have been awarded, they never looked back.
Mata added a second from close range five minutes after the restart and Javier Hernandez put the result beyond doubt 15 minutes later, before substitute Januzaj wrapped up a comfortable win at the death with the help of a deft assist by the Spain international.
The win lifted United into sixth place, with Tottenham not in action until Monday evening, but Moyes refused to be drawn on the prospect of a Europa League campaign.
He said: "The job I would like to do is finish as high up the table as we can.
"I don't know where it's going to be, I don't know what's going to happen, but I want to try to keep winning the games and see where we end up.
"If we get into that situation, then we can make a call on it."