The top-ranked nation achieved victory soon after tea on the last day to complete a highly satisfying result against their closest challengers in the world test rankings.
"India are always a big challenge and it was always going to be important for us to do well against them," Smith said at the post match presentation
It was also fitting farewell for South Africa all-rounder Jacques Kallis who made a century in his final test.
South Africa were 59 without loss in their second innings after India had been bowled out for 223 earlier in the day, failing to offer much resistance after being precariously placed at 68 for two overnight.
Only Ajinkya Rahane offered a bright spot for the Indians, coming within four runs of his maiden test century.
He was the last Indian wicket to fall, just after lunch on Monday, swinging wildly on 96 with only the last tail-ender Mohammed Shami left in support.
South Africa took just 11.4 overs to knock off the required runs with Alviro Petersen 31 not out and Smith unbeaten on 27 after a six and a four from the last two balls of the game.
Spinner Robin Peterson emerged as the unlikely match hero, overshadowing his fast bowling colleagues with a four-wicket haul in India's second innings to add to brisk the 61 runs he scored on Sunday, batting at number nine in South Africa's first innings.
But nine wickets in the match for fast bowler Dale Steyn earned him the man of the match award and he became the second fastest player to reach 350 test wickets.
On his last day of test cricket, Kallis, regarded as South Africa's finest cricketer, was not troubled in the slips and did not bat in the second innings.
"Last day of Test cricket for me," he tweeted before play. "I have so many wonderful memories and stories, thanks to my family, friends, team mates and fans. Tough day."
But there was more of a clinical edge than heavy emotion on Monday as South Africa went about their task with business-like efficiency to emphasis their status as the top-ranked test team.
Kallis was taken by his team mates on a lap of honour, waving to the crowds and being forced at one stage to down a can of beer.
The win ended a run of four successive test defeats in Durban for the hosts, who last weekend came desperately close to a world record fourth-innings chase before settling for a draw in the first test in Johannesburg.
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