Italy had been unable to take advantage of a yellow card to Japan lock Samuela Anise in the fourth minute but the first half remained in their favour and they opened the scoring in the 19th when winger Tomasso Benvenuti finished off a long-range try.
Hooker and captain Leonardo Ghiraldini then scored from in close to give the visitors a 12-3 lead at the break.
Flanker Jake Polledri added a third try shortly after the restart to give a dominant Italy a 16-point advantage that should have been enough to hold on.
Japan, however, stormed back after they were sparked by centre Will Tupou's try that was followed by another by rampaging number eight Amanaki Mafi within five minutes to drag the side back to 19-17.
Italian flyhalf Allan, however, then slotted two crucial penalties to give his side an eight-point cushion with a little more than five minutes to play.
Japan fullback Kotaro Matsushima completed the scoring in the 80th minute.
While Japan may be disappointed not to have sealed a 2-0 sweep of the series, the nature of their second half fightback will give the 2019 World Cup hosts confidence ahead of their clash with Georgia in Aichi next week.
(Reporting by Greg Stutchbury in Wellington; Editing by John O'Brien)
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