South Africa asked India to bat on Friday and the visitors posted 8-202 in their 20 overs, before bowling out their hosts for 141 in 17.5 overs for a comprehensive victory.
India's total was boosted by a brilliant 107 from 50 balls from Samson, even if their innings did stall towards the end.
Samson smashed 10 sixes and seven fours as he tore into the bowling at the small Kingsmead ground, rattling along at a strike rate of 214 to provide more than half his team's total.
"The amount of hard work he (Samson) has put in over the last few years, doing those boring things again and again, he is reaping the fruits," India captain Suryakumar Yadav said.
"He is putting the team first. Even when he was in the 90s, he was looking to hit fours and sixes. That's what separates him."
At 2-167 in the 15th over, India looked on course for a score well in excess of 200, but managed only another 35 runs in 32 balls for the loss of six wickets after Tilak Varma was dismissed for 33.
Seamers Marco Jansen (1-24 in four overs) and Gerald Coetzee (3-37) were the pick of the home attack.
India's legbreak bowlers stifled the South African reply as their innings never managed to gain momentum.
Varun Chakravarthy took 3-25 as he picked up the key wickets of Heinrich Klaasen (25) and David Miller (18), while Ravi Bishnoi recorded figures of 3-28.
"We wanted to get off to a better start with the bat and that's where we lost the game," South Africa captain Aiden Markram said.
"Sanju played incredibly well, put our bowlers under pressure. When a guy is striking like that, it is pretty hard to stop him and you have to take your hat off."
The second match of the series will be played in Gqeberha on Sunday.
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