De Kock showed composure beyond his years as he hit a career-best 135 in a South African total of 358-4. Dale Steyn and Ryan McLaren then took three wickets apiece as India was bowled out for 217.
It was an unpleasant welcome for an India side whose lack of preparation in South African conditions was clear in both their batting and bowling.
By contrast, de Kock needed little time to settle in on his home ground, finding the boundary regularly in a 152-run opening partnership with Hashim Amla, who scored 65.
The pair scored at more than five runs an over to set the platform for South Africa's innings, before Amla played on off the bowling of Mohammed Shami, who took 3-68 in his 10 overs.
The only disappointment in South Africa's innings was Jacques Kallis (10), but it was one that the hosts quickly brushed aside as AB de Villiers joined de Kock for a partnership that reinforced the home side's dominance.
De Kock went to three figures in 101 deliveries and added a further 35 in 20 balls, before he was caught and bowled by Virat Kohli.
That brought de Villiers together with JP Duminy for the final assault, which saw the hosts smash 100 runs off the last six overs.
"The thing that pleases me the most is that we really earned the right to show a bit of flair at the end," de Villiers said. "We always knew that if we took it to 35 overs with wickets in hand, they've got the kind of bowling attack that you can put under pressure at the end."
De Villiers was bowled by Shami for 77 in the final over, while Duminy finished unbeaten on 59 from just 29 deliveries as India's bowlers were punished for missing their lengths on a hard pitch.
The second ODI of the three-match series takes place in Durban on Sunday.