In the ascendant for the first time in the five matches when they were 68/0 chasing 271 towards the end of the second session, the touring team lost 10 wickets for 56 runs to slump to a 13th defeat in their last 15 Tests in Australia.
Rohit is the front-runner for leading India in the longest format as well because he was appointed the Test vice-captain by the Indian selectors ahead of the recently concluded South Africa series.
Kohli took India to the top of world Test rankings.
India had lost a three-match series to South Africa under Kohli's captaincy.
Chasing 212 in tough conditions at Newlands, South Africa were 60/1 in the 21st over when Elgar got the reprieve, but with the Indian camp busy with the DRS controversy the hosts went on to score 40 runs in the next eight overs.
Only Virat Kohli himself averaged above 40 among the India players.
Keegan Petersen scored 82 as South Africa beat India by seven wickets on a spiteful Newlands pitch to win the series 2-1.
The brittle Indian batting line-up meant the visitors failed to conquer South Africa for the eighth successive tour spread over a little over 29 years.
The Indian players were upset by the DRS decision that ruled in favour of South African skipper Dean Elgar.
Cheteshwar Pujara (9) and Ajinkya Rahane (1) were dismissed cheaply in the first half an hour.