The South Africans held a small halftime lead (20-17) over the enterprising Scots after a thrilling opening half, which saw both sides displaying some good attacking rugby.
On the day he collected his 38th cap to pass Butch James as South Africa's second most capped outside-half, Pollard ran in a first-half try and nailed two conversions and three penalties as Rassie Erasmus' Springboks followed New Zealand's Murrayfield success of 12 months ago as only the second away team in 12 matches to triumph on Scottish soil.
But while South Africa were a man short, Pollard put over another penalty to become South Africa's third-highest test point scorer with 336 career points, and restore a 23-20 lead.
"We had opportunities to win the game, so we're pretty frustrated, but we've got to give South Africa credit for the way they defended and slowed up the ball".
"In our view, Wales are definitely the most hard opponent we will face on this tour", emphasised Erasmus.
Scotland skipper Laidlaw said: "We are very frustrated and couldn't get any speed of ball".
"I really haven't seen it", said Erasmus, whose team finish their European tour against Wales in Cardiff next Saturday.
"The maturity of this team is starting to show because we are now winning games from tight situations".
Ireland went through a period between 2004 and 2009 where they beat the Boks three times in a row - all in Dublin - while France have also achieved that figure once, in a spell between 2005 and 2009 (twice at home venues, once at Newlands).
The breakdown was however a key area where the Springboks performed admirably, according to Erasmus: "We did well at the breakdown, especially our work at the defensive breakdown where we won managed to win vital turnovers at important times".
Pollard made the first and hit the post with the second.
"We focused really hard and worked on all the things that didn't go right last week".
If we do play them come the World Cup, I think they know it won't be an easy game, that we will be there to front up and won't take a backwards step.
Springbok coach Rassie Erasmus on Monday described Wales as their "most hard opponent" of their November tour to the United Kingdom and France.
Scotland vice-captain Stuart McInally says South Africa are "the most physical team in world rugby" ahead of the Springboks' visit to Murrayfield on Saturday.