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Victory would have catapulted the home side into the top eight of the world rankings and retained for them second-seed status for the 2011 World Cup draw.
But a try for replacement Jaque Fourie and nine points from the boot of Ruan Pienaar cancelled out Nathan Hines' first-half try for Scotland as the Springboks added to their rather more easily-achieved successes in Edinburgh in a World Cup warm-up last August and in November 2004.
This second defeat of the autumn series means Scotland, left to rue a succession of missed penalty kicks from Phil Godman and Dan Parks, could now feasibly be grouped with two powerhouses such as New Zealand and France when the draw is made for the tournament in two years' time.
The opening to the match was characterised by unforced errors from both sides, most prominent among them Mike Blair allowing his first kick of the afternoon to be charged down and Bryan Habana, with just one try in his previous 10 Tests, knocking on when under no pressure.
The flow to the game was not helped when South Africa were forced into a change after just five minutes, Bismarck Du Plessis limping off with a leg injury to be replaced by Brian Mujati.
Scotland had to make a switch of their own six minutes later when main goalkicker Chris Paterson, having bravely taken a high ball under severe pressure, had to be replaced by Hugo Southwell.
Parks also entered the fray at this point in a blood substitution for Godman and the Glasgow man promptly missed two relatively easy penalty opportunities as first Schalk Burger was penalised for not using his arms in a tackle on Ross Ford and then Mujati was adjudged to have dived over the top of a ruck.
Scotland's profligacy was matched by Springbok stand-off Pienaar, who missed a straightforward penalty at the midway point in the half.
To the audible relief of the Murrayfield crowd, a patched-up Godman returned in place of Parks - who had endured a miserable seven minutes on the pitch - and the Edinburgh number 10 kicked his side ahead in the 28th minute from directly in front of the posts after Tendai Mtawarira had come in at the side.
The visitors quickly responded with a jet-heeled break down the left by Jean De Villiers and Conrad Jantjes but terrific scrambling by Scotland held the Springboks up before Burger was penalised for coming over the top by English referee Dave Pearce, who had infuriated the visitors throughout the half.
Moments later Blair made a scything break round the fringe of a ruck and fed the lively Godman, who evaded the retreating South African defence before being hauled down just short of the line by Pierre Spies.
Scotland's forwards recycled the ball several times before lock Hines crashed to break his country try drought at Murrayfield a minute before the break, Godman adding the extras to make it 10-0 at half-time.
South Africa were enjoying their best period of the match early in the second period and although Scotland's defence held firm, Pienaar did reduce their advantage with a penalty after John Barclay was caught offside.
The visiting number 10 brought his team to within four points with another penalty on 55 after Allan Jacobsen was penalised for not rolling away.
The penalty count was now turning against Scotland and that gave their opponents comprehensive dominance of territory and possession.
That superiority was turned into points when Fourie finished superbly in the corner despite another terrific tackle from Southwell.
The try just before the hour mark gave South Africa the lead for the first time and Hadden responded by sending Scott Gray on for former captain Jason White in the back row.
After Godman missed a difficult penalty kick to regain the lead for his side, Pienaar stretched South Africa's lead to 14-10 with three more points following a Scotland infringement at a ruck.
Hadden's men were certainly not a beaten side though and could have got to within a point had Godman not missed another eminently kickable penalty after Pienaar was caught offside.
Scotland exerted considerable pressure on the Springbok line in search of a priceless try but it was not forthcoming and now they must wait for their World Cup fate.