After beating New Zealand 28-0 in the semi-finals, the Springboks romped to victory, scoring five tries to one.
Wing Seabelo Senatla scored twice in the final while Kwagga Smith also crossed after bagging a hat-trick in the semis, as the South Africans moved to 37 points, second place in the standings, behind Fiji (39).
"We didn't play our best in Australia but this was a fantastic event for us," South African captain Kyle Brown said. "We've worked hard on our defence all day and this means a lot to all of us."
South Africa will host the third round of the series in Port Elizabeth next weekend. There are nine rounds in total for the men with the top four placed teams automatically booking places for the 2016 Rio Olympics, when sevens rugby will be included for the first time.
Australia moved to third place, one point ahead of New Zealand, who finished fourth in Dubai.
The Australians produced an extraordinary comeback just to reach the final, overturning a 19-0 deficit to beat Fiji 29-24 semi-finals.
Nick Malouf scored in the final minute of normal time to level the scores at 24-24 before Greg Jeloudev crossed for the winner in extra-time.
"For us to get to a Cup final was a terrific effort ... we showed an incredible amount of character to beat Fiji," Australia head coach Geraint John said.
New Zealand won the women's final with another remarkable comeback against Australia on Friday.
Sarah Goss, playing with a broken finger, sealed the victory with a try in the last minute as the New Zealanders came from 17-0 behind to win 19-17.
Dubai was the first round of the women's series, which also doubles as an Olympic qualifier. The next round is in Brazil in February.
(Editing by Ian Ransom)
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