The Swedes dominated the encounter from the first whistle and could have taken the lead within five minutes but midfielder Caroline Seger saw her effort from distance come back off the crossbar.
Thomas Dennerby’s side were ahead in the seventh minute, though, when captain Fischer’s strike from the edge of the penalty area deflected off South Africa defender Refiloe Jane and looped over helpless goalkeeper Roxanne Barker into the net.
The lead was doubled on 20 minutes after Marie Hammarstrom picked out team-mate Dahlkvist with an accurate cross and the latter converted from close range.
Within seconds, Sweden extended their advantage even further and ensured their Olympic campaign would start with a win. Fischer found Schelin free behind the South African defence and the forward poked the ball past Barker to make it 3-0.
Finally sparked into action, South Africa almost responded immediately but Modise shot wide after being afforded too much time and space in the Sweden box, in the last genuine action of the opening period.
Modise more than made up for that miss 15 minutes into the second half, however, beating Sweden ‘keeper Hedvig Lindahl from almost the halfway line to give the South Africans a slim chance of mounting a comeback.
Any hopes of securing a result were dashed within three minutes, though, as Schelin claimed her second goal of the match to restore Sweden’s three-goal cushion, which was rarely threatened during the rest of the encounter.