But the tourists did not lack spirit and sensationally drew level again through Dewi Lake with 13 on the pitch, only for Biggar to marginally miss the posts with the conversion when he could have secured a late lead. Instead, Biggar's knock-on at the other end allowed Willemse to kick the Springboks to a memorable triumph to begin this three-Test series, which continues in Bloemfontein next Saturday.
The SANZAAR nations claimed wins in the opening weekend of the July tests with New Zealand, Australia and Argentina all climbing the world rankings.
Australia ended an eight-game losing run against England despite a red card to Darcy Swain in the 34th minute claiming a 30-28 victory while South Africa left it late to down Wales 32-29 in a thrilling come-from-behind victory.
New Zealand stormed to a 42-19 win over Ireland while Argentina completed the SANZAAR full house with a 26-18 victory over Scotland.
After the All Blacks' win over Ireland, South Africa knew anything less than a win would see them lose their top ranking.
Two Louis Rees-Zammit tries gave Wales a commanding lead, but Dan Biggar headed to the sin bin shortly before the interval, and Bongi Mbonambi powered over following the restart. Malcolm Marx also crossed, and the visitors appeared to have collapsed after Cheslin Kolbe's try was followed by a yellow card for Alun Wyn Jones – the awarding of which caused some confusion.
Rees-Zammit went from hero to zero as his desperate attempt to stop a South Africa try saw him join Jones on the sidelines, and Wales were down to 12 men and behind when Rhys Carre's intervention resulted in a penalty try.
An early try for Keith Earls looked to represent the perfect start for them, particularly against a home team whose build-up had been ransacked by a COVID-19 outbreak, requiring ex-Ireland boss Joe Schmidt to step into their coaching ranks. But a barnstorming run by debutant Leicester Fainga’anuku helped get Jordie Barrett over the line in response, sparking a fluid All Blacks passage, with finishes for Sevu Reece, Quinn Tupaea and Savea setting a 28-5 advantage at the break.
Garry Ringrose responded after the interval to give Ireland hope, but a superb solo second for Savea sealed the game,before Pita Gus Sowakula crossed for a try on debut and Bundee Aki nabbed a late consolation finish in the closing stages.
Following their win at the Optus Stadium, Australia have swapped places with England. The Wallabies are now in fifth on 84.68 points with England sixth on 83.74.
Argentina are now above Scotland in the rankings following their 26-18 win in Jujuy. Los Pumas have improved their rating by 0.82 of a point, taking them up to seventh on 80.98 points, while Scotland drop to eighth, on 81.4 points.
Wales and Japan, meanwhile, remain in the top 10, on 79.27 and 77.90 points respectively. Fiji began their bid for a sixth title with an emphatic 36-0 win against Tonga in Suva. The win did not improve their rating, though.
Italy are now just one place below Fiji after jumping two places to 12th on the back of their impressive 45-13 win against Romania in Bucharest. Georgia and Samoa both dropped down a place due to the Azzurri’s progress.
Romania lost as many places as Italy gained, resulting in the USA and Uruguay improving their ranking by one place.
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