South Africa were 107 for three at lunch, with AB De Villiers on 59 not out and captain Faf du Plessis unbeaten on 37, after being 12 for three.
Kumar took wickets in each of his first three overs to get his side off to a dream start.
He dismissed Dean Elgar, Aiden Markram and Hashim Amla to have South Africa, second behind India on the world Test rankings, reeling.
Du Plessis won the toss and decided to bat on a well-grassed pitch, a decision which he admitted was tricky.
Elgar, South Africa’s leading batsman during 2017, edged the third ball of the match to be caught behind by Wriddhiman Saha for nought.
His opening partner, Markram, fell in Kumar’s next over, leg before wicket for five, before Amla, on three, edged an attempted back foot drive and gave Saha a second catch.
De Villiers, who spent almost two years out of Test cricket after injury and a self-imposed exile, started the fightback when he hit four fours off Kumar’s fifth over.
With Du Plessis providing solid support, De Villiers went for his shots and reached his fifty off 55 balls with ten fours.
By lunch, the pair had added 95 runs off 127 balls in an unbeaten fourth wicket partnership.
