Olesen, who has not played since the start of February after surgery to his left hand, had set the clubhouse target of 13 under par with a three under par final round of 68.
But Coetzee, who had led for the majority of the final day until a bogey on the 17th hole, birdied the closing hole for a round of 69 to match that score and take the tournament to extra holes.
After his eagle attempt lipped out on the first extra hole and both players made birdies, Coetzee then took advantage second time round with another four, compared to Olesen’s par five, to claim his third European Tour title.
The victory, Coetzee’s second of the season on The European Tour after March’s Tshwane Open, moves him into the top ten on The Race to Dubai, and with the campaign only 19-events-old, he is the fifth multiple European Tour winner so far in 2015, joining Branden Grace, Anirban Lahiri, Andy Sullivan and Rory McIlroy.
Singapore’s Mardan Mamat birdied two of the closing three holes for a final round of 67 to finish third on 12 under par. Fittingly, it meant the Sunshine, European and Asian Tours were all represented in the top three in the first tournament to be tri-sanctioned by the three Tours.