Aiden Markram's unbeaten 69, aided by 26no from Tristan Stubbs, enabled them to reach 3-170 off 33 overs in reply to Afghanistan's modest 169 in the match played at a neutral venue in Sharjah.
Afghanistan had skittled South Africa out cheaply to win the first match on Wednesday and then handed the visitors a 177-run thumping on Friday.
They were unable to replicate their form on Sunday, even after again winning the toss and electing to bat in the third ODI.
Their innings was dominated again by the powerful hitting of opener Rahmanullah Gurbaz, who scored 105 in Friday's comprehensive victory which put Afghanistan 2-0 up in the three-match series.
This time, he fell 11 short of another century, smashing 89 off 94 balls before being snapped up on the boundary by a flying catch by Reeza Hendricks off the bowling of Andile Phehlukwayo.
But the Afghanis were undone by poor decision making and a little misfortune as they suffered three run-outs.
Rahmat Shah was run out when a ball that was hit back down the wicket by Gurbaz was deflected by the bowler Lungi Ngidi onto the shoulder of the stranded Shah and onto his wicket.
Captain Hashmatullah Shahidi and Ikram Alikhil were slow in making their ground and run out by quick thinking in the field with Afghanistan slumping to 7-132 before Allah Ghazanfar contributed an unbeaten 31 off 15 to take them past 150.
South Africa were always on course to reach the target even after losing their opening three batters for 80.
Markram was the aggressor with Stubbs in a supporting role as their unbeaten 90-run partnership saw South Africa home.
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