Following their 23-18 win over Wales in Cardiff on Saturday, the Springboks remain narrowly behind the All Blacks in second spot on the latest World Rugby rankings.
The Springboks collected two-tenths of a rating point to close to just 0.03 of a point behind their old rivals.
The Boks had to beat Wales by more than 15 points to reclaim the top position they last held until a fortnight ago.
Earlier in the day, the All Blacks beat Italy 47-9 but gained no points because the Italians are ranked No 14.
Elsewhere, fourth-placed England narrowed the gap between themselves and Australia following a 69-3 win over Tonga at Twickenham.
The Wallabies lost 15-13 to Scotland in Edinburgh on Sunday, but the Scots remain seventh.
Ireland stay fifth after a convincing 60-5 win at home to 10th-ranked Japan and France are just under three-quarters of a point behind them in sixth after seeing off eighth-ranked Argentina 29-20 in Paris.
2. South Africa - 91.33
3. Australia - 86.26
4. England - 85.44
5. Ireland - 84.96
6. France - 84.25
7. Scotland - 83.27
8. Argentina - 80.30
9. Wales - 79.99
10. Japan - 78.50