The Italians join hosts and defending champions New Zealand as well as Canada, England, France and Australia in booking their place in the competition's last eight.
Melissa Bettoni's 78th minute try sealed the victory after Michela Sillari scored two second half penalties as Andrea Di Giandomenico's side moved past a resilient Japanese side, who exit the tournament with a third consecutive loss.
The Italians went in front with nine minutes on the clock, Aura Muzzo bursting down the left flank before being stopped short of the line by the Japanese defence, only for Maria Magatti to pick up possession and score.
But the Japanese responded with 10 minutes remaining in the half when, after a sustained period of pressure deep in the Italian half, Kyoko Hosokawa sidestepped her way past the defence to cross the line.
Sillari slotted her penalty between the posts with three minutes remaining in the half to give the Italians a slender lead at the interval.
Japan pulled level again through Ayasa Otsuka's penalty nine minutes after the resumption but Sillari's successful kicks in the 54th and 67th minutes gave the Italians a fragile advantage.
Hooker Bettoni powered over with two minutes remaining to put the result beyond doubt and take her team into the next round of the competition.
Later on Sunday Pool B leaders Canada will take on the United States later while tournament favourites England face South Africa in Pool C.Â
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