Amanda Ilestedt's 90th-minute winner gave Sweden a 2-1 win over South Africa in their Women's World Cup Group G match on Sunday after a fortuitous equaliser from Fridolina Rolfo had cancelled out Hildah Magaia's opener.

Under pouring rain in the New Zealand capital, Ilestedt jumped highest and squeezed the ball home to save her team's blushes after they were left frustrated by the African champions for much of the opening hour of the game.

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The result left the third-ranked Swedes top of their group, before Italy and Argentina play their opener in Auckland on Monday.

"South Africa made it hard for us, but I think we grew into the game and got better and better. In the second half we played better, but a victory in the opening game is what counts," Ilestedt said.

South Africa, ranked 54th, were looking for their first ever World Cup win on their second appearance at the tournament, having exited in the group stage in 2019 without picking up a point.

They kept their more fancied opponents at bay in the first half, as a frustrated Sweden side controlled possession but could not find the finishing touch, and threatened on the counter.

Captain Refiloe Jane's brilliant long-range attempt floated over the crossbar, while Sweden struggled to create clear-cut chances, with Filippa Angeldal drawing the only save from the goalkeeper in the first half with a tame effort.

Zecira Musovic had parried away Thembi Kgatlana's shot but Magaia got to the rebound before Sweden defender Jonna Andersson and bundled the ball over the line two minutes after the break, scoring South Africa's second ever World Cup goal.

But Johanna Rytting Kaneryd's cross skewed off defender Lebohang Ramalepe and bounced into the net off Rolfo to hand the Swedes a lifeline in the 66th minute.

Peter Gerhardsson's side pushed for a winner but they were denied by South Africa's resolute defending, until Ilestedt met Kosovare Asllani's corner with a strong header.

"We're so used to being in such situations where things don't work, (and thinking about) what are we going to do," Gerhardsson said.

"It's no coincidence that we decided the match on a set piece, it's no coincidence because that's what we practice a lot."

Sweden will take on Italy in Wellington on Saturday after South Africa face Argentina in Dunedin on Friday. South Africa coach Desiree Ellis said there were plenty of positives to take from their opener.

"We knew that they were going to be a challenge at set pieces and I thought we handled that really well," Ellis said. "Even though it was a loss, we're very proud of the way we played.

"We have the speed and skill up front, we have the skill in midfield and defensively we were really good. That is a big plus for us."