South Africa need a win to secure first spot in Pool B and set up a quarter-final with either Wales or Australia at Twickenham on October 17.
USA have not won any of their games in this section, but victory this afternoon would still keep them in the running for third position and therefore automatic qualification for the World Cup in 2019.
From shorter distance, USA had their second penalty in the 15th minute, but Niku Kruger could only strike the post as South Africa kept their seven-point lead in tact.
Burger, who was heavily involved early on, took a knee to the jaw in the 18th minute as both teams showed their physical prowess, but no penalty was awarded. Three minutes later, Bryan Habana and Blaine Scully were both out of the game following a collision in the middle of the field.
South Africa thought that they had scored their second try of the match in the 25th minute when Jesse Kriel burst towards the line, but replays showed that he was just short after excellent work from Kruger.
South Africa did move onto 12 points in the 27th minute, however, with a penalty try, before Pollard converted for 14-0.
USA continued to struggle to make their mark in the latter stages of the first half, with South Africa leading comfortably at the interval. South Africa have won all three of the previous meetings between the two teams by at least 23 points.