The 2019 semi-finalists showed why they remain heavyweights of the women's game as Amanda Ilestedt, Fridolina Rolfo and Stina Blackstenius scored in the space of seven minutes at the end of the first half.
Italy, who had recorded clean sheets in six of their previous 13 World Cup matches, conceded a third when Blackstenius, another Arsenal player, finished from close range.
In front of a crowd of 29,143, it went from bad to worse for Le Azzurre when Ilestedt added the fourth - her third goal of the tournament - with another header from another corner.
And substitute Rebecka Blomqvist added the fifth in the 95th minute.
"I really want to pay tribute to the players," said Sweden boss Peter Gerhardsson. "Not for the first time I'm impressed by these players."
Andersson, the former Chelsea defender, was a real threat with her corners as she provided two assists prompting Gerhardsson to add: "We have been good at set-pieces for a long time."
Sweden will face one of the United States, the Netherlands or Portugal in the knockout stage.
Italy remain second in the group with three points from two games, but need to defeat South Africa next Wednesday back in Wellington (08:00 BST) to make sure of progressing in the tournament.Sweden turn on the style
Former finalists Sweden needed a 90th-minute winner from Ilestedt to overcome South Africa in their opening group game.
They had no such problems dispatching Italy in New Zealand's capital.
The World Cup ever-presents, who are ranked third in the world behind defending world champions the United States and Germany, sent out a powerful message they could go deep into yet another tournament.
After reaching the semi-finalists in France four years ago, they made it to the Olympic final two years ago before making the semi-finals of Euro 2022.
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With the team based about half an hour's drive from Wellington, Sweden have attracted lots of local support in New Zealand's capital.
The locals in the Saturday night crowd lapped up the goals as Sweden showed their ruthless side, with defender Ilestedt now joint leading scorer at the tournament with Brazil forward Ary Borges.
Italy do not have long to recover before they face South Africa in a match they must win to make sure of joining Sweden in the last 16.
They secured a narrow 1-0 win over Argentina in their first group game as Cristiana Girelli headed an 87th-minute winner.
But they were completely overwhelmed in this all-European encounter, with their defending from corners a major concern for boss Milena Bertolini.
"For the first half an hour we gave them a hard time, we tried to fight them but didn't succeed," said Bertolini.
"We were a bit fragile mentally because after conceding the first two goals we were not able to stay calm.
"We need to work on our mental strength."
After the men's national team failed to qualify for the past two World Cups, the women are flying the flag on the world stage.
Yet they need a much-improved performance against South Africa to stay in this tournament.
Le Azzurre started confidently and should have taken the lead when Sofia Cantore's attempt was spilled but Lucia di Guglielmo fired into the side-netting.
But once Ilestedt opened the floodgates, Italy were second best.
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