Sweden, ranked fourth in the world, got off to a cracking start in Coventry on Wednesday night, hitting the crossbar twice before captain Nilla Fischer got a deflection off Refiloe Jane to put them ahead in the seventh minute.
After hitting the post again, the Swedish women stretched the gap with two goals in quick succession midway through the first half.
Lisa Dahlkivst tapped in a close-range effort in the 20th minute, and seconds after the restart Lotta Schelin slid the ball in from the edge of the box.
The South African women managed to gain some composure and Portia Modise created their first chance in the 22nd minute but her shot sailed wide to the right.
Banyana skipper Amanda Dlamini also made a tame long-range attempt soon after but it was comfortably controlled by Swedish goalkeeper Hedvig Lindahl.
Star striker Noko Matlou had perhaps Banyana's best opportunity of the opening period, but she failed narrowly to connect with a cross in the area.
Sweden took their foot off the pedal for the remainder of the first half but the South Arican women struggled to take advantage and they went into the break 3-0 behind.
With Banyana still finding their composure against a Swedish side that seemed content to sit back in the second period, Modise netted a stunning strike on the hour mark.
Catching Lindahl off her line, the veteran striker blasted a shot from 45 metres out that lobbed over the keeper's head to give the South Africans their first goal of the tournament.
The Swedes hit back immediately, however, when Schelin connected with a cross to tap in at the near post, securing brace.
Modise's strike seemed to wake the Swedish women from their slumber as they pushed forward again, but the Banyana defence, anchored by goalkeeper Roxanne Barker, managed to keep them out for the rest of the match.
Banyana face Canada in their second Group F match in Coventry on Saturday.
The Games officially start with the opening ceremony in London on Friday night.
Top women's scorer
Meanwhile, Brazil's forward Cristiane became the top women's scorer at the Olympics after netting her 11th tournament goal in Brazil's 5-0 rout of Cameroon on Wednesday.
Cristiane surpassed retired Germany star Birgit Prinz, who had 10 Olympic goals.
The 27-year-old Brazilian scored the record-breaking goal in the 80th minute after a perfect pass from Marta, picking up the ball inside the area and dribbling past the goalkeeper before hitting the open net.
"This is special, I knew I was tied and needed just one more to get the record for myself," said Cristiane, participating in her third Olympics.
She said the achievement meant even more considering she didn't even know if she was going to be playing at the London Games because of a right shoulder injury she sustained shortly before the tournament. She had already injured the same shoulder in late 2010.
"All I can think about is the time I spent trying to recover from my recent injury, practicing alone and not knowing if was going to be able to play in the Olympics," she said. "I was sidelined for four weeks and nearly got dropped from the squad."
Because of the injury, Cristiane started on the bench and entered the match at half time to replace Thais Guedes.
"I had been training well but when you get to play it's different," she said.
Just before the goal Cristiane had another great opportunity to score but her close-range shot was saved by the Cameroon goalkeeper.
She also helped set up the penalty kick converted by Marta in the 73rd at the Millennium Stadium in Cardiff, Wales.
"She is one of our best players," Brazil coach Jorge Barcellos said. "We knew she could come through with a performance like that for us even from the bench."
Cristiane is trying to help Brazil win its first major title. The Brazilians had to settle for the silver medal in the last two Olympics after losses to the United States in the final. It also was second to Germany in the 2007 World Cup in China. – Sapa, Sapa-AP