Oosthuizen, despite a late bogey, shot a 6-under-par 66 in the final round for a 72-hole total of 16-under 272. Jamison, who entered the fourth round with a five-stroke lead, shot even-par 72 Sunday and was 15 under for the tournament.
Thongchai Jaidee, who shot 68 Sunday, finished third overall at 14-under. Padraig Harrington came in fourth at 12-under and Danny Willett and Julien Quesne tied for fifth. Harrington and Willett each matched Jaidee's 68 Sunday while Quesne shot 71.
Jamieson seemed in control with the big lead and birdies Sunday at Nos. 3 and 4 but he suffered a double bogey 6 at the fifth hole. He had 10 consecutive pars before a bogey at the 16th. A closing birdie got him back to even on the day.
Meanwhile, Oosthuizen, who struggled with a six-bogey round that led to a 2-over 74 Saturday, pulled back into contention with birdies at 2 and 3 and two more at 6 and 8 in making the turn in 32.
He added birdies at 10 and 11 that moved him into the lead. A birdie at the par-5 14th hole gave him a two-stroke cushion that survived his bogey at the 16th hole.
It was the 10th professional win overall for Oosthuizen and sixth title on the European Tour. He has at least one European Tour win each year since 2010.