Tendulkar struggled for 88 minutes and 62 balls in scoring 14 before he was out in the last over before tea, adjudged lbw to a ball that reverse-swung sharply back into his pads.
It completed a poor afternoon for India, who scored only 48 runs for the loss of four wickets between lunch and tea.
The slide continued after tea with Graeme Smith's decision to bring back Steyn proving a master stroke, with the fast bowler having Kumble caught at gully in the first over of his second spell.
Khan was run out by a good throw from deep cover by De Villiers after being sent back by Karthik, who then watched helplessly from the other end as the innings subsided.
Smith and De Villiers started South Africa's run chase confidently, putting on 36 before De Villiers was caught behind off Khan for 22.
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