Thanks to their in-form, spin-dominated bowling, India have not had to chase a 140-plus target all tournament.
The 173-run target they needed on Friday appeared all the more difficult against an attack containing fearsome paceman Dale Steyn and destructive leg-spinner Imran Tahir.
Kohli, however, again proved why he is considered his team's batting mainstay, hitting a 44-ball 72 not out to help India secure victory with five balls left as South Africa continued their sorry record of never having advanced beyond the semis at either a 50-over or 20-over World Cup.
"I'm glad to have played an important knock in the semi-final," man of the match Kohli told reporters.
It was a well-paced innings from the right-hander from Delhi who did not hit a boundary in his first 17 runs but smashed two sixes and five fours to accelerate when the time was right.
India tried not to take too many risks after losing both openers in order to ensure they had wickets in hand for the late run chase.
They needed 51 off the last five overs and when they got safely home the ploy had worked.
"I know the deeper I bat the more chance we have of winning. One (leading) batsman has to be there until the 20th over," Kohli said.
"It was not as easy as it appeared. There was pressure but it was important not to reveal that to the opposition.
"They have a world class attack. If they sense the smallest mistake or if you allow them some space they take the game away from you," Kohli added.
It was a smooth run chase by the Indian batsmen who initially treated Steyn and Tahir with respect and targeted the other bowlers.
Earlier, captain Faf du Plessis celebrated his return with a sparkling 58 and JP Duminy made a brisk 45 not out to help South Africa to 172 for four at the Sher-e-Bangla National Stadium.
Opting to bat first South Africa lost both openers while reaching 44 in the sixth over before Du Plessis, who missed Saturday's group match against England due to a slow over-rate suspension, added 71 runs with Duminy in 8.4 overs.
Even after the skipper departed Duminy played aggressively, hitting three sixes and a four in his 40-ball knock.
Off-spinner Ravichandran Ashwin was the pick of the Indian bowlers, giving away 22 runs in four tidy overs and claiming the key wickets of Du Plessis, Hashim Amla (22) and the dangerous AB de Villiers (10).
The South African bowlers could not emulate Ashwin's discipline as they conceded nine wides.
"In a World Cup it's important you do the small things and the basics well," said a glum Du Plessis.
"That was definitely one of the things tonight that's probably not a match-changer but definitely put us on the back foot.
"Nine extra balls, not just extra runs you give away, but you also have to consider the runs they score off those extra balls," added Du Plessis.
"When you want to win close games like this you've got to make sure you get even the small things right and unfortunately tonight we did not."