The five time European Tour winner was all class in recovering from his disappointing first round with scores of 67-68-66 to get to 4-under for the week and T7.
Only three players bettered Rumford's score on the final day and only four were ahead of him in each of the second and third rounds.
Rumford had a horror time at the tournament in 2015 when he was forced to withdraw after 36 holes with a digestive blockage.
He eventually underwent surgery to remove 30 cm of his small intestine before spending 17 days in two different hospitals, the second of which he later described as 'like a prison camp'.
But despite that experience Rumford showed a liking for the course through 36 holes last year with rounds of 64-70 seeing him T10 prior to his withdrawal.
His opening round aside, Rumford continued what has been an encouraging start to the season with his fourth consecutive made cut and first top-10 finish.
Six Australians began the week in South Africa with Jason Scrivener and Dimi Papadatos the only other two to make the cut.
Scrivener fought hard to make the weekend after a weather delay Friday afternoon but struggled at the weekend, a Sunday 76 dropping him 21 places down the leader board to T63.
Papadatos finished on the same score with rounds of 71-72-73-73 while Daniel Gaunt and tournament invitees Ben Eccles and Lincoln Tighe all missed the cut.
Headlines at a glance
- The Hayne Plane en route for the Fiji International 30.09.2016
- Yenda beer tees up new PGA partnership 29.09.2016
- Jeffress and Lawson in winning form 29.09.2016
- Hend heads back to Asia 28.09.2016
- Women’s Holden Scramble crowns 25,000th participant 28.09.2016
- Felton’s Fiji return marks anniversary of Professional debut 28.09.2016
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Jeffress and Lawson in winning form
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Hend heads back to Asia
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