Banyana made a pacey start, but nearly fell behind when Stina Blackstenius controlled a through pass before testing Banyana's Andile Dlamini on 11 minutes.
The hosts had to wait 30 minutes to get their first shot on goal after Rhoda Mulaudzi squandered a good opportunity in the box following a well-driven through ball by Thembi Kgatalana.
The South Africans had earlier on provided another caution to get on the front-foot through a first-time shot by Kgatlana that unfortunately went over the top.
After a snoozing first half, the opening minutes of the following segment didn’t provide any serious efforts but Dlamini was called to keep out a good shot from Blackstenius.
Banyana handed out their first threat of the half when Refiloe Jane’s shot required Sweden's number one to pull off a fine save on 57 minutes.
The ninth-ranked side were inches away from pole position after Olivia Schough’s first time half-volley draw a save off Dlamini in the final minutes.
As the clocked winded down, chances opened up more though for the away side as a rasping drive from Hanna Glas ended with a shot off the crossbar.
Into added time, Jermaine Seoposenwe almost stole the show from a free-kick but the attempt swerved around the post as the clash ended goalless.