AB de Villiers has retained the top spot with 883 points but Amla, with scores of 38 and 119 in the series, closed the gap to 28 points.
Kohli, however, will get a chance to move up the order when he takes the field against Sri Lanka in a five-match series starting Nov 2 as only two points separate the second and third ranked batsmen.
The biggest mover was 33-year-old New Zealand wicketkeeper-batsman Luke Ronchi who has risen 52 places to 62nd after his impressive showing against South Africa.
In the ODI team rankings, South Africa reclaimed the summit spot after winning in New Zealand. They had entered the series trailing Australia by one point but moved to the top following their 72-run victory in the second ODI in Mount Maunganui Oct 24.
This is the first time in five years that South Africa have surged to the top of the ODI team table. They last enjoyed the spot in September 2009 before losing the status to Australia following they first round elimination from the ICC Champions Trophy.
The ODI team rankings:
1. South Africa 115
2. Australia 114
3. India 113
4. Sri Lanka 111
5. England 107
6. Pakistan 98
7. New Zealand 96
8. West Indies 96
9. Bangladesh 69
10. Zimbabwe 58
ODI batting rankings:
1. AB de Villiers (South Africa) 883
2. Hashim Amla (South Africa) 855
3. Virat Kohli (India) 853
4. George Bailey (Australia) 802
5. Kumar Sangakkara (Sri Lanka) 800
6. Mahendra Singh Dhoni (India) 757
7. Tillakaratne Dilshan (Sri Lanka) 739
8. Quinton de Kock (South Africa) 739
9. Shikhar Dhawan (India) 722
10. Ross Taylor (New Zealand) 702