The world Test champions lead the two-match series 1-0, and even a draw in Guwahati would secure their first series win in India since 2000.
India, having lost the opener in Kolkata, their fourth defeat in six home Tests, will need to bat long to avoid another loss.
The Proteas reached 107-3 at the first break, after losing three wickets in the morning session, with Tristan Stubbs on 14 and Tony de Zorzi on 21 at the crease.
Play in Guwahati began 30 minutes early due to early sunsets, with intervals reversed—shorter tea before lunch.
South Africa resumed at 26-0, after bowling India out for 201 on day three, taking a 288-run lead in the first innings. They opted not to enforce the follow-on.
Left-handed opener Ryan Rickelton hit three fours in the first session before he fell to Jadeja's left-arm spin while attempting another hit over cover but got caught out. He made 35.
Jadeja (2-20) bowled the other overnight batter, Aiden Markram, for 29 before fellow spinner Washington Sundar dismissed skipper Temba Bavuma for three.