The Proteas won the toss and opted to bat, going on to make 196 for eight in their 20 overs at the western Indian city’s Wankhede Stadium.
JP Duminy top-scored for South Africa, hitting 67 off 44 balls. His impressive knock included six fours and three sixes.
Left-handed batsman Quinton de Kock stylishly played his way to 56 runs before retiring not out.
Hardik Pandya was the pick of India’s bowlers, grabbing three wickets.
India’s run chase got off to a bad start with opener Rohit Sharma going for ten and Virat Kohli managing just one before being caught off only his second ball.
Shikhar Dhawan was India’s highest scorer with 73 while Suresh Raina notched 41 and captain Mahendra Singh Dhoni recorded 30 as the home side got into their groove.
But in the end they fell just short on a total of 192 for three.
In the day’s earlier game, New Zealand won the toss and elected to bat with captain Kane Williamson smashing a 63.
Williamson’s knock included nine fours as the Black Caps made 169 for eight in their 20 overs.
The second highest scorer for New Zealand was Ross Taylor who finished on 19 not out.
England opener Jason Roy then powered his way to 55 off 36 balls, including seven runs and two sixes, while Alex Hales notched 44 as England reached 170 for four with four balls remaining.
Leg-spinner Adil Rashid was the standout performer of England’s bowling attack, grabbing three wickets for just 15 runs.
India play New Zealand on Tuesday in the first Super 10 group-stage game of the tournament.
England are in action against the West Indies on Wednesday before facing South Africa on Friday in the Proteas’ first match of the championship.