The third-ranked Swedes join title contenders Spain and former champions Japan in reaching the knockout rounds with a match to spare.
Three goals in seven minutes in the first half did the damage as Italy struggled to deal with Sweden's set pieces and aerial threat.
Arsenal defender Amanda Ilestedt scored twice -- both headers -- with Fridolina Rolfo, Stina Blackstenius and Rebecka Blomqvist also on the scoresheet.
Sweden came back to beat South Africa 2-1 in their opening game of the tournament thanks to a last-minute Ilestedt winner -- again with her head.
But they were far more comfortable against an Italy side who can still qualify from Group G, having defeated Argentina 1-0 to start their campaign.
The Sweden-Italy encounter in front of just under 30,000 in Wellington was the starter to the main course of the day.
France came into the tournament as one of the favourites, but a country known for so long as being the great underachievers of women's international football underwhelmed in being held 0-0 by Jamaica.
In contrast, Brazil smashed Panama 4-0 to open their World Cup with Ary Borges hitting a hat-trick.
Another slip-up for France in Brisbane would leave them in danger of an early exit from Group F.
In the final match of Saturday, Jamaica will be hoping to win a World Cup game for the first time when they play Panama.
- Kerr comeback -
Co-hosts Australia are another in danger of failing to go any further in the tournament but their hopes were given a big boost on Saturday when skipper Sam Kerr declared herself available.
Prolific Chelsea striker Kerr, the face of the World Cup in Australia and New Zealand, suffered a calf injury on the eve of the tournament and missed the Matildas' first two games.
The Australians squeezed past Ireland 1-0 thanks to a penalty to open their campaign but were then stunned 3-2 by Nigeria.
With a critical encounter against Olympic champions Canada looming on Monday, the 29-year-old fronted the media in Brisbane to say: "I am going to be there, I am going to be ready."
But Kerr declined to say how much of a part she will play in the clash in Melbourne.
"I would love to tell you guys everything but you know being in sport a long time that that's a massive thing that the opposition wants to know," Kerr said.
Meanwhile, European champions England sweated on the fitness of key midfielder Keira Walsh after she was stretchered off in their win over Denmark on Friday with what looked like a serious knee injury.
There has been a spate of knee injuries in women's football and England were already missing captain Leah Williamson and Euro 2022 Golden Boot winner Beth Mead for that reason.
- Caicedo fitness doubt -
A tight Group A will be decided on Sunday in what looks set for a thrilling conclusion.
Switzerland lead with four points and are in pole position to advance. They play co-hosts New Zealand in a sell-out in Dunedin.
New Zealand are level on three points with debutants the Philippines, who play former champions Norway at the same time in Auckland.
Norway, who sit bottom of the group with one point, can still qualify but they must win at a minimum -- and do it without star striker Ada Hegerberg, who is injured.
Also in action on Sunday are one of the favourites, Germany, who face Colombia in Group H.
The Colombians could be without teenage star forward Linda Caicedo after she went down in training on Thursday holding her chest.
Colombia coach Nelson Abadia on Saturday called it "an episode of tiredness, a bit of stress over her debut in a senior World Cup".
"It was just an episode and she is ok now," he added. "Linda has overcome the event.
"Whether she will play, we have 24 hours or a bit more to decide."
In the other Group H game South Korea face Morocco.
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