Karthik, who has rode his performance in the recent Indian Premier League to make a comeback into the national team, set up victory with his maiden T20 fifty.
"I am feeling very secure in this setup. In the last game things didn't go according to plan, but I went and expressed myself today," man of the match Karthik said.
Relishing his role as a finisher, he said, "I think DK is thinking a little better. He is able to assess situations better and that comes with practice."
Batting great Sunil Gavaskar was all praise for Karthik on TV commentary and said, "If DK is not on that flight to Melbourne then it is a big surprise."
Australia will host T20's showpiece tournament later this year.
Karthik, a wicketkeeper-batsman who scored 330 runs at a strike rate of over 183 for IPL side Royal Challengers Bangalore, lifted India from a precarious 81-4 in the 13th over to take the attack to the opposition.
He put on a crucial 65-run stand with Hardik Pandya, who hit 46 off 31 deliveries, as the pair hammered the opposition bowlers to all parts of the ground.
Karthik smashed nine fours and two sixes as he surpassed his previous best of 48 to make India plunder 73 runs from the final five overs.
"Really happy with the way Hardik put up a show. DK went for the kill right away and that gave us the positivity," said skipper Rishabh Pant.
In reply, the visitors were never in the chase after skipper Temba Bavuma retired hurt on eight with an injured elbow and the team soon lost two wickets.
Wicketkeeper-batsman Quinton de Kock was run out for 14 and Dwaine Pretorius out to Avesh in the fifth over.
Wickets kept tumbling and Harshal Patel raised the pitch at the nearly packed house after he bowled the dangerous David Miller for nine.
Avesh returned to take three wickets including Rassie van der Dussen for 20 in the 14th over to flatten South Africa on a seemingly tough pitch to bat.
Spinner Axar Patel got the ninth wicket to end South Africa's innings in 16.5 overs as Bavuma, who sat in the dugout with an ice pack on his elbow, did not come back out to bat.