Kohli's career-best 254 not out in India's second successive win in the three-match series moved him to within one point of Smith in the International Cricket Council Test chart.
Smith replaced Kohli at number one last month following his blazing Ashes series against England and after the Indian star made a golden duck against the West Indies.
The Australian, who only returned to Tests in August after a year-long ban for ball-tampering, is out of action in the five-day format until November 21 when Australia host Pakistan.
Kohli regained lost ground against the struggling South Africans in the current series as he registered his seventh Test double century, joining England great Wally Hammond and Sri Lanka's Mahela Jayawardene.
He also went past Don Bradman's tally of 6,996 runs in 52 Tests that led India to register their record 11th straight Test triumph at home. Australia had two streaks of 10 wins in a row.
"I'm just happy to be where I am. Putting the team in a commanding position is the only thing I strive for," Kohli, who tops the ODI batting chart, said after India took an unassailable 2-0 lead in Pune on Sunday.
"Of course I enjoy scoring runs, but if they come in a winning cause, nothing like it."
Kohli meanwhile has even won praise from former Pakistan speedster Shoaib Akhtar who praised the Indian for his "fearless" brand of cricket.
"He will score 250 in future as well," Akhtar said on his YouTube channel. "Kohli has learnt from his mistakes and has become a good captain."
Boring' pitches
South Africa skipper Faf du Plessis will be hoping to give his team more of a chance from the get-go in Ranchi after losing the toss in the first two Tests.
This allowed India to amass a mammoth first-innings total of 502 in Visakhapatnam as South Africa's bowlers toiled, a feat outdone in Pune when the hosts declared on 601.
This prompted former England captain Michael Vaughan to call Indian Test pitches "boring".
"The first 3/4 days the contest is far too in favour of the bat... needs more action for the bowler," Vaughan tweeted last Friday.
Dean Elgar's 160 has been the visitors' only standout show in the series so far.
Paceman Kagiso Rabada said the up-and-coming team -- following the retirements of Hashim Amla and Dale Steyn -- should pick up the positives and move ahead.
"Our team is fresh and young, so the best thing we can do is look at where we can improve and remember our strengths and build on them," he said.
He added, "From a physical point of view we need to execute our skills and from a mental point of view, we need to believe we can do it in certain situations. It's a balance we're working on."