Scotland's Paul Lawrie, who had started the round in second spot, carded a 73 to drop to sixth overall along with Austria's Markus Brier.
BBC: SPORT | Golf | Battling Casey closes on leaders
Scotland's Elliot Saltman shot a 67, while at Kilmarnock Barassie his brother Lloyd fired a first-round 66 to be one behind Austria's Markus Brier.
BBC: Olazabal faces fight to make Open
Wood, 23, who was the top amateur at the 2008 Open at Royal Birkdale where he finished fifth, had started the day two shots off the lead held by Oosthuizen and Austria's Markus Brier.
BBC: Oosthuizen beats Wood in play-off for Africa Open win
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