A defiant 97 by Ashwell Prince could not prevent India from achieving their first Test win in three tours of South Africa here on Monday.
Prince and Shaun Pollock, virtually the only South Africans who shone in the match, put on 67 for the seventh wicket, their team's highest partnership of either innings, to delay India's victory celebrations.
The stand was ended by Kumble, who bowled Pollock for 40. Kumble then trapped Andre Nel leg before before bowling Prince when the left-hander went down the pitch and misjudged the flight. Kumble took three for 54.
India's win was set up when they bowled out South Africa for 84 in the first innings when opening bowler Shanthakumaran Sreesanth took five for 40.
Sreesanth, who followed up with three top order wickets in South Africa's second innings, was unable to add to his wicket tally as South Africa's last five wickets fell for 115 Monday. Sreesanth had match figures of eight for 99.
South Africa's slim hopes of pulling off a miracle win suffered an early blow when Mark Boucher was out to the 15th ball of the morning without adding to his overnight score of 23. Boucher played across a full-length ball from left-armer Zaheer Khan and was given out leg before.
Pollock played an attacking innings, hitting Khan out of the attack with some powerful blows, including a hooked six. He made his runs off 41 balls with six fours and a six.
But the introduction of the experienced Kumble effectively snuffed out South Africa's hopes of getting anywhere near a victory target of 402.
Following the dismissal of Nel, Prince played some attacking shots and seemed on course for his fifth Test century before being bowled three runs short. He defied the Indian bowlers for 327 minutes, faced 223 balls and hit 11 fours.
It was his second near-miss at the Wanderers. Last season he was out for 93 against Australia.
South Africa were bowled out for 278, the highest total of the match, when Makhaya Ntini was caught at point off Zaheer Khan after the second new ball was taken.
The second match in a three-Test series starts in Durban on Dec 26.
India 249 and 236 beat South Africa 84 and 278 (A Prince 97, Pollock 40, Kallis 27; Kumble 3 for 54, Sreesanth 3 for 59, Zaheer 3 for 79)