"They can win it, but they've got to play the game of their lives and eliminate the errors," Hastings, who won 65 caps for his country, told Reuters on Tuesday ahead of the Pool C game between Tonga and Namibia in Exeter.
"We have seen both against Japan and the USA, that they create opportunities but they've made errors.
"South Africa will put Scotland under pressure for a full 80 minutes, and it is how they deal with that because they are not going to find enough space."
Scotland were trailing at halftime against the United States on Sunday, having failed to finish a number of clear try-scoring chances in the opening period.
Hastings said they will have to be far more clinical against the Springboks, and improve their kicking game.
"When they have the opportunity to put a winger away or to put Stuart Hogg down the flanks, the accuracy of the pass has got to be there," he said. "These last two games they have got away with it, but in tighter games they won't.
"Their kicking game is not as good as other international teams. Their kick chase and kick retention is poor. You can see when other teams are fielding the ball - the Australians and Wales are very good at this - they are retaining possession, but also securing possession when the ball is kicked to them."
Earlier on Tuesday Scotland called up flanker Blair Cowan to replace lock Grant Gilchrist, who was ruled out of the tournament after being injured against the United States.
Hastings said that if Scotland's only other openside flanker John Hardie does not recover from a head injury, Cowan could find himself thrust straight into Saturday's team where the breakdown will be key.
"There has been concern about John Hardie and this head knock, and all it needs is another head knock and he is probably out.
"Maybe Scotland have called it on the basis that they have just got to have cover at open-side. If Scotland are to put down the Springboks, the key to that is undoubtedly an openside flanker... ultimately it is all about the breakdown and putting pressure on the breakdown."
Of some comfort to Scotland fans, Hastings is confident that the country's key playmaker Finn Russell will play on Saturday.
"He has done his ankle ligaments, simple as that. He was strapped and latterly, he was getting a support padding put in that I have had many a time on an ankle ligament. He'll be alright...I reckon he'll start."
(Editing by Mitch Phillips)
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