The Swedes' three goals came in the first half, with the first goal scored in the first seven minutes, while the other two were scored in the space of two minutes as Sweden were all over Banyana.
Portia Modise scored a consolation goal for Banyana in the 60th minute and this revived the fighting spirit of the South African women team to deny the world fourth ranked side to score more than five goals.
Back at home, South Africans rallied behind their women national team by watching the match on their televisions, while those in the match venue were flying the country's flags high to show their support.
Ahead of the game, government wished Banyana Banyana all the best. "We believe that the team has prepared properly for the games ahead and we are confident that they will win all the matches and make South Africa proud," government spokesperson Jimmy Manyi said.
Banayana will play against the seventh world ranked Canadian team in Coventry on Saturday, before their biggest test of all, against world champions, Japan in Cardiff, on Monday.