The Cheetahs hooker crashed over early from short range before sprinting away with an interception to double his tally and bury Scotland in the second half as the Springboks continue to win, and win the hard way, having battled to victory in Ireland last week.
Rising star Henry Pyrgos came off the bench sparking a real fight back by the home side - scoring with his first touch after one of many Scotland line-outs deep inside the South African 22 opened up, allowing the scrum-half to dart over.
The Springboks looked to be on the ropes for the final 20 minutes but, in an all too familiar result for the home fans, Scotland were unable to put points on the board and now lose any hope of a top-eight IRB ranking, and qualification as a seed for the next World Cup.
While the visitors led 6-3 after 20 minutes through two penalties from Patrick Lambie, neither side appeared able to wrestle full control of the game in what became a battle for territory.
With first-half possession more or less level, the bruising back-row play of Willem Alberts and Francois Louw at the breakdown proved to be the difference. Scotland - without the injured Alasdair Strokosch and Ross Rennie - lost the fight at the breakdown, and fell behind in the penalty count.
On 21 minutes Lambie waved off one of those penalties, and put the ball in the corner. Shortening the line-out, the Springbok pack worked a rolling maul perfectly with Strauss almost walking over for his first.
Lambie slotted a third penalty on the half hour and the second half opened with Scotland chasing down the 14-3 deficit and looking to stretch the game as Mike Blair pushed a loose pass to a wide pod of forwards on his own ten metre line.
The ball was easily read by Strauss who showed everyone that Schalk Britz is not the only Springbok hooker who can run in the open-field - demonstrating good pace as he beat the Scottish cover.
The pass was Blair’s last act, making way to Pyros, who within minutes helped the Murrayfield crowd - subdued by the 21-3 scoreline - find their voice.
Turning down a kickable penalty, Stuart Hogg put the ball into the right corner – and as captain Kelly Brown leaped at the tail, the Springbok defence opened up for Pyrgos who needed no second invitation to sprint through and bring his side back to within two scores.
The try brought Scotland to life, and some great running by Brown, the recalled David Denton and prop Ryan Grant frequently brought the home side to within 20 metres of the Springbok line.
Turning down several penalties in order to set-up a drive, Scotland were often their own worst enemies – Ross Ford misfired on a crucial throw five metres out, and Tim Visser – who crossed twice against the All Blacks – knocked on with the line at his mercy.
Heyneke Meyer’s side will no doubt be happy to get out with a win – just their second away victory of the year – as they go to Twickenham to face an England side also unbeaten this autumn, while Andy Robinson has only a much improved defensive effort as consolation, when, perhaps with greater composure, his side could have come away with another historic Murrayfield upset.