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.
Canada confirmed themselves as winners of Pool B with a 29-14 victory over the United States in Auckland.
Early scores from Emily Tuttosi and Alex Tessier put Canada in control and, although Alev Kelter reduced the deficit in the 19th minute, Paige Farries' try gave Kevin Rouet's team a 19-7 lead at halftime.
Olivia DeMerchant scored on the hour mark to earn the Canadians a bonus point and Mikiela Nelson dived over the line in the final seconds as her team guaranteed they will be seeded higher than England in the next round.
Top-ranked England muscled their way into the quarter-finals with a 75-0 win over South Africa which stretched their record winning streak to 28 Test matches.
England finished atop Group C with an unbeaten record after wins over Fiji, France and South Africa.Â
Their 13-7 win over France from which they failed to take a bonus point cost them a higher seeding but was still one of the loudest statements of form in the group stage.
- with AP
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