United boss David Moyes opted for a mixture of youth and experience, with youngsters Michael Keane, Ben Amos and Fabio da Silva joining Michael Carrick, Ashley Young and Patrice Evra in the starting lineup.
There was a familiar face in the Kitchee lineup, meanwhile, with former Fulham defender Zesh Rehman selected in the middle of the home side's defence.
Anderson and Young both came close with 15 minutes on the clock, but United had their first goal less than a minute later when Danny Welbeck smashed a low effort into the bottom corner from inside the box.
Zaha had a guilt-edged chance to make it 2-0 after 19 minutes, but somehow the England international blazed over the crossbar from close range. United had their second moments later, however, when Chris Smalling headed a Tom Cleverley cross into the back of the net.
It was 3-0 after 26 minutes when Zaha found Fabio, who arrowed a powerful first-time effort into the bottom corner with United utterly dominating proceedings.
Christian Annan remained the main outlet for the hosts, but the midfielder could not test Ben Amos in the United goal despite some good opportunities in the final third.
Januzaj continued to impress in the early stages of the second period, but the Belgian could not add his second in quick succession when presented with the opportunity inside the box.
Anderson came close to extending the lead moments later, but it was Kitchee who added a second after 68 minutes when Alex Alkande burst into the box before slotting a low effort into the bottom corner.
There was time for United to make it 5-2 in the final 10 minutes, however, with Jesse Lingard curling a stunning effort into the top corner to register his fourth goal on tour.