South Africa's hopes of claiming their first ever Women's World Cup point were agonizingly dashed by a late Swedish fightback in Wellington on Sunday.

The Banyana Banyana, the African champions, looked on course for a famous result after Hildah Magaia's strike put them ahead early in the second half.

But the highly-ranked Europeans showed their pedigree to turn the game around and break African hearts.

Fridolina Rolfo leveled midway through the second period before Amanda Ilestedt's stoppage time header snatched a 2-1 comeback win.

Magaia slotted home to spark early scenes of jubilation among South African fans after Thembi Kgatlana's shot was parried into her path.

The seismic moment arrived just three minutes after the restart, courtesy of Kgatlana's electrifying run down the left flank for South Africa.

Kgatlana unleashed a shot at Sweden's goalkeeper, Zecira Musovic, who could only parry the ball into the path of Magaia, seizing the opportunity to slot home from close range.

But the celebrations were cut short as Magaia immediately suffered an injury and left in tears after the goal.

Sweden capitalized on her absence to equalize courtesy of Rolfo's fortuitous effort that looped in off defender Lebohang Ramalepe.

The European giants pressed relentlessly for a winner, with substitute Caroline Seger going close.

Yet just as a historic draw loomed, up rose Ilestedt to meet a late corner and silence South African hopes in heartbreaking fashion.

The defeat means the wait for Banyana's first World Cup point goes on after this cruel twist.

But they can take pride from pushing the world's elite all the way before late luck deserted them once again.