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
- World Cup of Golf hospitality now on sale 25.05.2016
- Golf Trader - PGA Member David Fearns (Jnr) 25.05.2016
- Big Aussie assault at second Senior Major 25.05.2016
- McCardle, Wood to build on good China start 25.05.2016
- Strong Aussie contingent at Czech Challenge 25.05.2016
- Scrivener reaps rewards with Wentworth start 25.05.2016
Big Aussie assault at second Senior Major
Four Australians will be in the field for the year's second senior major which tees off this week in Michigan.
PGA Tour China
McCardle, Wood to build on good China start
After making good starts in the first event of the season to be in the top-10 on the PGA TOUR China Order of Merit, Max McCardle and Chris Wood will b...