The victory in the last eight clash was South Africa's first in a knockout match at a World Cup and earned them a date with New Zealand or West Indies in Auckland next week with a spot in the final up for grabs.
The Proteas will probably have to win the semi-final to finally bury their reputation as World Cup 'chokers' but they went some way to removing the tag with the rout of the 1996 champions, who they restricted to 133 runs off 37.2 overs.
Under-fire opener Quinton de Kock led the way with an unbeaten 78 from 57 balls as the South Africans comfortably reached their target with 32 overs to spare at the cost of only the wicket of Hashim Amla.
After losing the toss and being sent into the field, South Africa's highly rated but under-performing pace attack quickly removed both openers but it was spin-bowling that did the most damage to Sri Lanka's cause.
Duminy took three for 29 and Imran Tahir four for 26, the pair combining to break the back of the Sri Lanka innings with four wickets at the cost of just two runs in three overs to reduce the islanders to 116-8.
The spell included the ninth World Cup hat-trick, Duminy dismissing Angelo Mathews (19) with the final ball of the 33rd over and returning to send back Nuwan Kulasekara (1) and debutant Tharindu Kaushal (0) with the first two deliveries of the 35th.
When Kumar Sangakkara was dismissed soon afterwards, Sri Lanka's hopes of reaching a third successive World Cup final looked all but gone.
Sangakkara, who had been looking for a record fifth successive century, scored a measured 45 but was forced to throw off the shackles as the wickets tumbled around him and holed out in the deep off paceman Morne Morkel.
A heavy shower appeared out of the blue as if to mourn the final one-day innings of one of the game's great batsmen and the players came off the pitch for a 23-minute rain break.
It only delayed the inevitable, however, and de Kock and Amla were soon at the crease playing with the freedom allowed to a batsman chasing such a low target.
Amla departed for 16 but de Kock and Faf du Plessis (21 not out) ensured that skipper AB de Villiers, who scored 162 not out in his last innings at the SCG last month, could keep his powder dry for challenges to come.
Tahir's four victims included Mahela Jayawardene to leave the other retiring Sri Lanka batting great with a tally of four runs in his final innings in the 50-over format.
(Editing by Sudipto Ganguly)
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