Rossouw, who failed to trouble the scorers in the previous two innings in the series, struck exactly 100 not out off just 48 balls as the Proteas made their way to a total of 227-3 in their 20 overs after being inserted by home skipper Rohit Sharma at the toss.
India lost early wickets in the mammoth run-chase and eventually laboured to 178 all out to fall to defeat but the home team still claimed the three-match series 2-1.
The left-handed Rossouw found good support from opener Quinton de Kock, who hit 68 from 43 balls while Tristan Stubbs, pushed up the order for some time in the middle ahead of the T20 World Cup, scored 23.
David Miller, fresh from an unbeaten century in the defeat in the second T20I, finished off the innings in grand style, striking three maximums in the final over to end on 19 not out of just five balls.
South Africa's management will still be concerned about the batting form of captain Temba Bavuma, who once again struggled as he made three off eights balls to go with his two ducks in the three-match series.
The tourists made a near-perfect start with the ball to defend the mammoth total with paceman Kagiso Rabada bowling Rohit without scoring in the first over.
Wayne Parnell then trapped Shreyas Iyer lbw for single and the hosts were starting down the barrel and continued to lose wickets at regular intervals in pursuit of quick runs.
Dinesh Karthik hit a flurry of boundaries in his 46 of 21 balls before going for one too many and was clean bowled by spinner Keshav Maharaj.
India found themselves 120-8 in the 13th over but a few late cameos from tail-enders Deepak Chahar (31) and Umesh Yadav (20) made the score more respectable as India were bowled out with none balls to spare.
Both teams will have been pleased with certain combinations and will look to improve some aspects ahead of the T20 World Cup in Australia starting later this month.