South Africa, who lost the first two matches of the series, were put in to bat first in Indore.
The left-handed pair of Quinton de Kock (68) and Rossouw (100 not out) put on 89 runs for the second wicket to lay the foundations of a challenging total.
Rossouw, who hit eight sixes, then got going with Tristan Stubbs in another big partnership of 87 and surpassed his previous best of 96 not out to reach his hundred in 48 balls.
De Kock started aggressively with a six and four off Mohammed Siraj in the second over before skipper Temba Bavuma fell for three to Umesh Yadav, extending his batting slump after he got ducks in the first two matches.
Rossouw joined De Kock as South Africa reached 48-1 in the first six overs of powerplay.
Rossouw survived a dropped catch on 24 by Siraj in the deep as the ball popped out of his hands for a six. De Kock made his second successive fifty with a hit over the fence off Yadav.
The pair hit eight sixes between them before the partnership ended with De Kock’s run out in his attempt to steal a second run.
Rossouw reached his fifty in 27 balls with a six off Axar Patel and kept up the batting charge with Stubbs, who was warned by pace bowler Deepak Chahar for backing up at the non-striker’s end when on 13.
Rossouw finished unbeaten and David Miller, who hit a 100 in the second T20, smacked three straight sixes in the final over from Chahar to score an unbeaten 19 off five balls.
India need 228 to sweep the series in the absence of Virat Kohli and KL Rahul, both of whom have been rested in the final match for India ahead of the T20 World Cup starting later this month.
