Tendulkar stroked an elegant 146 as India were bowled out for 364, a lead of just two. Harbhajan Singh then claimed two late wickets as the hosts reached 52 for two in their second innings. The series is tied 1-1.
Tendulkar, who scored seven Test centuries last year, brought up his hundred after lunch by top-edging a hook off Morne Morkel for six.
He took India from 28 for two to 341 for eight before his 314-ball stay was ended by a fine delivery from Morkel who beat him with a ball that was angled in before nipping away to hit the top of off stump.
Steyn, who finished with five for 75, had produced an inspired two-wicket burst with the second new ball straight after lunch.
The fast bowler struck when he trapped Cheteshwar Pujara (2) leg-before with an unplayable delivery that pitched on leg-stump and then swung away late to hit the batsman on the back pad, plumb in front of the stumps.
Steyn was quick to follow up with the wicket of Indian captain Mahendra Singh Dhoni, who edged another fine away-swinger to be caught at third slip for a duck.
Another fantastic delivery had Harbhajan groping to no avail as the ball swung into off stump. But somehow the bails failed to fall.
Harbhajan went on to hit a valuable 40 in a 76-run seventh-wicket stand with Tendulkar.
Steyn had threatened to tear through the Indian batting in his first spell of the day but went wicketless as the batsmen played and missed time and again.
South Africa reached 50 without loss before Harbhajan struck.
He won an lbw appeal against captain Graeme Smith (29) in his second over before nightwatchman Paul Harris fell for a duck when he shouldered arms to the off-spinner and was also given out leg-before.
