Kohli, on his birthday, got to the landmark in 119 balls, including 10 fours, at Kolkata's Eden Gardens.
It had taken him 277 innings to score 49 hundreds at this level compared to the 438 required by Tendulkar.
Kohli's 101 not out was the centrepiece of unbeaten tournament hosts India's 326-5 in their 50 overs.
Together with Shreyas Iyer, who made 77, he shared a third-wicket partnership of 134 after India captain Rohit Sharma (40) had won the toss on what turned out to be a tricky pitch.
Kohli, the only survivor from that 2011 Nagpur line-up, was celebrating his 35th birthday on Sunday and even when a lone fan had the crowd chuckling as he started belting out an out-of-tune rendition of 'Happy Birthday' - the batsman turned a deaf ear to the commotion.
That laser focus sums up the way India has approached this World Cup as they remain the only unbeaten side among the 10 participating nations, having won all eight of their group matches.
A sea of blue-clad India fans kept filing into the 66,000-capacity ground for several hours before the 2pm local time start as excitement mounted for the top-of-the-table showdown that many believe will be a dress rehearsal for the Nov. 19 final.
With a place in the semi-finals already bagged by both teams before Sunday's contest, India put on a dazzling show with bat and ball to keep the home fans roaring at full throttle for hours and hours.
The 25th meeting between the two teams since India last hosted tournament showed just how far Kohli has come since his contribution in that 2011 Nagpur tussle with South Africa amounted to one measly run.
On Sunday, he avoided the temptation of going for the big hits over the boundary as he scored a record-equalling 49th ODI century - a milestone he now shares with Indian great Sachin Tendulkar.
"Every opportunity to play for India is big one for me. To be able to do that on my birthday, in front of the whole crowd, it's stuff of dreams, something that as a child you wish had happened," Kohli said.
While Tendulkar scored his 49th century in his 451st ODI innings, Kohli reached the landmark in his 277th innings, a fact noted by Tendulkar who celebrated his 50th birthday in April.
"Well played Virat. It took me 365 days to go from 49 to 50 earlier this year. I hope you go from 49 to 50 and break my record in the next few days. Congratulations!!" Tendulkar said on social media platform X.
When Kohli reached triple figures with a single off Kagiso Rabada in the 49th over, he left the organisers to mark the occasion with some pyrotechnics while he simply removed his helmet, looked skywards, acknowledged the cheers and within seconds he was back marking his crease.
His unbeaten 101 off 121 balls included 10 fours but tellingly no sixes in a match that the Indians had started off at a fast and furious pace, with the hosts reaching 61-0 after five overs and then 91-1 after 10 overs.
Though it was inevitable that India would not be able to sustain the early 12.2 or 9.10 run rates over 50 overs, the 326-5 total they ended up posting proved to be insurmountable for South Africa.
Bowled out for 83, South Africa fell to their second defeat of the tournament after being stifled by Ravindra Jadeja's left-arm spin. Jadeja finished with five for 33.
