Sweden dominated from the start and was up 3-0 midway through the first half. Nilla Fischer gave Sweden the lead in the seventh minute and Lisa Dahlkvist made it 2-0 in the 20th before Schelin added the third just a minute later.
Portia Modise pulled one back with a long-range lob on the hour mark, before Schelin scored the fourth goal for Sweden in the 63rd.
The one-sided game was expected, with South Africa ranked 61st in the world while the Swedes are fourth and coming off a third-place finish at last year's World Cup.
Caroline Seger nearly put Sweden in front after five minutes, hitting the crossbar with a powerful volley. Instead it was Fischer who scored with a bit of luck two minutes later when her shot was deflected into the net off South Africa defender Refiloe Jane.
The Swedes continued to apply pressure and it paid off with two goals in two minutes.
The South Africans improved in the second half, and Modise opportunistically took advantage of Sweden goalkeeper Hedvig Lindahl being out of position. The Palace Super Falcons striker picked the ball up on the halfway line, strode forward and unleashed a 40-yard strike that soared over the backpedalling Lindahl.
But Sweden didn't buckle, and Schelin made it 4-1 just two minutes later, poking in Sara Thunebro's cross from close range.