Van der Dussen (75) and David Miller (64) put on 131 for the fourth wicket to drive the team’s chase of 212 in 19.1 overs and lead the five-match series 1-0 in New Delhi.
South Africa achieved their highest T20 run chase to end India’s bid to register a record 13th successive win in the format.
The win comes nearly two weeks after the end of the Indian Premier League which had over 10 Proteas players, including the title-winning Miller in the popular T20 tournament.
Van der Dussen played just three matches for Rajasthan Royals this edition but Miller remained key for Gujarat Titans’ triumph in their debut season with 481 runs in 16 innings.
“Myself having watched a lot of IPL games, having not got much of an opportunity to play, (I) had a pretty good idea what their bowlers would do and the conditions (at hand),” Van der Dussen told reporters.
“I spent two month here, been in the conditions, been in the heat, so had acclimatised to that and that goes to everyone. We had a lot of guys in the IPL this year and that’s helped us in the first game to adapt quicker and get over the line.”
The tourists overcame a pre-match blow when Aiden Markram was ruled out of the opener with Covid-19 in a series played without pandemic bubble restrictions.
Cricket South Africa said Markram, who played for Sunrisers Hyderabad in IPL, tested positive for the virus on Wednesday and is keeping “well” in his quarantine protocol.
Van der Dussen, who struggled initially but then accelerated, and Miller trumped Indian opener Ishan Kishan’s 76 off 48 balls that guided India to 211 for four after being put into bat first.
South Africa lost skipper Temba Bavuma for 10 in the second over of their chase but Dwaine Pretorius attempted to hit back in his 13-ball 29.
Pretorius’ departure and then Quinton de Kock’s wicket for 22 swung the momentum back in favour of India but Miller soon took charge.
He was punishing the bowlers as he hit left-arm spinner Axar Patel for a four and two sixes in a 19-run 13th over to silence the home crowd.
Miller reached his 50 in 22 balls and was named man of the match.
“It’s belief. I have been around for some time now but understanding and winning games give you a lot more confidence,” said Miller. “I am pretty open to bat anywhere. Just want to make a difference.”
Van der Dussen survived a dropped catch on 29 to record his seventh T20 half-century as he hit the winning boundary in his 46-ball innings.
Earlier Kishan lay the foundation for India’s total with key stands including an 80-run second-wicket partnership with Shreyas Iyer who made 36.
Kishan reached his fifty with a six off left-arm spinner Keshav Maharaj.
The diminutive Kishan smashed Maharaj for two sixes and two fours in the 13th over but got out caught on the last ball in another attempt to clear the rope.
Rishabh Pant, who made his captaincy debut for the national team after KL Rahul was ruled out with an injury on the eve of the match, smashed 29 and put together 46 runs off 18 balls with Pandya.
Pandya hit an unbeaten 31 off 12 balls as India finished with a flourish but the effort proved insufficient.
The second match is on Sunday in Cuttack.