Following on, the home team still trails by 259 runs, with eight of their second innings wickets intact.
After 23 overs in the second essay, India were 66 for 2, with Murali Vijay batting on 27 and Sachin Tendulkar on 15.
The Indian second innings, reeling under the shock of the collapse in the first, began in the worst possible manner. In the second over by Morne Morkel, Gautam Gambhir (1) witnessed a ball cut back in from outside the off and crash on to his stumps.
It was Gambhir's second successive failure; he scored just 12 in the first essay, having come into the series with a string of impressive scores and chasing a lot of records.
And when Virender Sehwag (16), the first innings centurion, edged Dale Steyn stright to Graeme Smith at first slip India were reduced to 24 for two.
Two balls later, Sachin Tendulkar was fortunate to survive a loud leg before appeal, after being guilty of not offering a shot.
Earlier, Dale Steyn ripped through the Indian batting line-up soon after the start of the third session. The 26-year-old had career-best figures of seven for 51 as India collapsed in their first innings from 221 for four to 233 all out in just 7.4 overs after tea.
It was the speedster's 13th Test haul of five or more wickets in an innings, and his second against India, after his five for 23 at Motera in 2008.
Steyn's impressive figures were also the best in his career thus far, eclipsing his six for 49 against New Zealand at SuperSport Park in 2007.
Morning session (94 runs, 27 overs, three wickets):
Resuming at 25 for no loss, India made a disastrous start on the third day, losing two wickets in the space of three overs.
South Africa got the early breakthrough they required, dismissing Gautam Gambhir in the second over of the day. Morne Morkel induced a faint edge off the left-hander's blade and Mark Boucher made no mistakes behind the stumps.
Gambhir (12) failed to add to his overnight total. India reduced to 31 for one after six overs.
Three overs later, Dale Steyn cleaned up Murali Vijay (4) to make it 40 for two.
And when Sachin Tendulkar (7) edged a Steyn delivery to Boucher it seemed a lost cause for India at 56 for three.
S Badrinath, making his Test debut after waiting in the wings for years, started with a lucky boundary off Steyn, an outer edge that went past the gully fielder.
India scored 42 runs off 13 overs, losing three wickets, in the first hour of the day's play.
Steyn (7-2-24-2) and Morkel (6-2-18-1), in their opening spells, had done the job that South Africa required them to do -- make early breakthoughs and put India on the backfoot.
However, the only solace for the home team came from the fact that Sehwag was still batting and looking good.
The dashing opener stood tall among the ruins and raced his way to his half century, his 22nd in Tests, off just 71 balls.
It was only his second fifty against South Africa, even though he has registered three century-plus scores against them, including the mammoth 319 at Chennai in 2008.
Badrinath also gained in confidence with each ball he faced, and the duo - their 50-run partnership coming off just 79 balls - ensured India didn't suffer any further damage before lunch.
After 27 overs in the morning session, India added 94 runs for the loss of three wickets -- in the second hour of play, the home side had made 52 runs from 14 overs and more importantly, not lost any further wicket.
At lunch, the home side had scored 119 for three, with Sehwag unbeaten on 63 and S Badrinath on 21.
Earlier, the visitors had put up a mammoth 558 for six declared in their first innings after batting for close to two days. A late declaration gave the hosts four overs to bat before stumps on day two.
Hashim Amla, with an unbeaten 253, and Jacques Kallis (173) were the most significant contributors to that South African total.
Post-lunch session (102 runs, 26 overs, one wicket):
In the third over after lunch, Sehwag survived a loud appeal. A Morkel delivery went past his blade and straight to Boucher, but the umpire (Ian Gould) remained unmoved.
Replays later suggested that the ball had pitched in front of Boucher and he had consequently not appealed.
Sehwag celebrated his good fortune with two boundaries in the next over by Morkel, the first an exquisite drive through the covers and the second a magnificent square drive.
JP Duminy was introduced into the attack in the seventh over after lunch and Sehwag welcomed him by dispatching his first ball -- a wide full toss -- to the cover boundary.
The 31-year-old soon reached his 18th Test hundred, his fourth against South Africa, with a single off Kallis.
India scored 59 off 14 overs in the third hour of play without any further loss.
Sehwag continued to attack, hitting Wayne Parnell for successive boundaries, the first towards third man and the next through covers.
However, the young Parnell had his revenge just two balls later, a momentary lapse of concentration costing Sehwag his wicket. The batsman could only shake his head in disbelief after slicing a wide delivery straight to Duminy at deep cover.
Sehwag's immaculate innings (109) came off just 139 balls and included 15 hits to the fence. He put on 136 for the fourth wicket with Badrinath. But his departure reduced India to 192 for four after the 47th over.
A few overs later, Badrinath went on to complete a well-deserved maiden Test half century with a cover drive off Morkel. The 29-year-old from Tamil Nadu had justified his selection.
It took MS Dhoni 15 balls to open his account. It took him another eight to hit his first boundary, to long on (off Duminy). And he survived just five more (after tea).
At tea, India had reached 221 for four (off 57 overs).
Post-tea session: India first innings (12 runs, 7.4 overs, six wickets):
The final session started and ended on a disastrous note for India.
India had regained lost ground in the second session but lost captain M S Dhoni (6) to the fourth ball of the first over (off Paul Harris) after tea.
To maintain the pressure the South African captain handed the ball to Steyn and the latter expressed his gratitude by ripping through the Indian tail.
The 26-year-old, who had already accounted for Murali Vijay and Sachin Tendulkar in the morning session, took over from the second over.
S Badrinath (56) was accounted for in the first ball, hitting straight to Ashwell Prince at short midwicket. Debutant Wriddhiman Saha (0) was cleaned up three balls later.
Saha was fortunate to get his Test debut owing to the many injuries the squad faced but was not fortunate enough to cash in on the opportunity and failed to justify his selection.
When Zaheer Khan (2) failed to guard his stumps in his next over, the 26-year-old had completed a fiver.
And when Steyn cleaned up Amit Mishra (0) in his third over and trapped Harbhajan plumb in front in his fourth, it was all over.
Steyn's figures in his lethal spell after tea read thus: five for three (off 3.4 overs).
India had added just 12 runs to their total after tea, losing six wickets in the process.
With a lead of 325 runs to bank upon South Africa enforced the follow-on, asking the home side to bat again.
India second innings:
Reeling under the shocking collapse, the second innings began in the worst possible manner.
In the second over by Morne Morkel, Gautam Gambhir (1) witnessed a ball cut back in from outside the off and crash onto his stumps.
It was Gambhir's second successive failure; he scored just 12 in the first essay, having come into the series with a string of impressive scores and chasing a lot of records.
And when Virender Sehwag (16), the first innings centurion, edged Dale Steyn stright to Graeme Smith at first slip, India were reduced to 24 for two.
Two balls later, Tendulkar was fortunate to survive a loud leg before appeal, after being guilty of not offering a shot.