Neither side had amassed more than 215 in an innings in the previous three Tests and India, who lead 2-0, were struggling on 66-3 and 139-6 in Delhi.
But Ajinkya Rahane hit 89 not out in half-century partnerships with Virat Kohli (44) and Ravindra Jadeja (24).
Recalled fast bowler Kyle Abbott (3-23) and spinner Dane Piedt (4-101) were the only South African wicket takers.
Piedt, 25, playing just his second Test, took four of the first five wickets to fall, including that of Kohli whose fluent 70-run stand with Rahane was ended in bizarre fashion.
The India captain, who won the toss for a fourth time, smashed a full-blooded sweep into Temba Bavuma at short-leg and after the ball ballooned into the air, wicketkeeper Dane Vilas dived forward to take the catch.
That sparked a mini collapse with three wickets falling for three runs before Rahane, who hit two sixes and nine boundaries in his first half century at home, steadied the innings and took India beyond 200.
Rahane was helped by Jadeja, whose 59-ball innings was ended by a smart Dean Elgar catch at midwicket off the bowling of Abbott.
South African Abbott, who had earlier bowled Cheteshwar Pujara and Wriddhiman Saha, conceded just 23 runs in 17 overs to continue his push to start the four-Test series against England, which begins on 26 December in Durban.

The men were believed to have been working on the northbound carriageway of the A361 at Gornhay Cross, Tiverton, when they were hit.
One was flown to Plymouth's Derriford Hospital, while a second Devon Air Ambulance flew the other man to the Royal Devon and Exeter Hospital.
The van driver has been arrested on suspicion of dangerous driving.
The condition of the two injured men, who are both in their 40s, is not known.
Devon and Cornwall Police said a third man was hurt in the incident, but he is described as the "walking wounded".
The Barnstaple-bound carriageway is expected to remain closed for several hours and diversions have been put in place.

Fisher, 60, who played Princess Leia in Star Wars, was taken ill on a flight from London to LA on Friday.
Passengers attempted to revive her with CPR and she was taken to hospital when the plane landed.
Co-star Harrison Ford said he was "shocked and saddened" by the news.
"Our thoughts are with Carrie, her family and friends," he said. Ford played Fisher's on-screen love interest in the franchise, and Fisher revealed earlier this year in a memoir that the pair had a brief off-screen romance.
Mark Hamill, who played Luke Skywalker, said he was sending "all our love" and Peter Mayhew, who played Chewbacca, tweeted his thoughts and prayers for "everyone's favourite princess".
Fisher's brother Todd said she was in intensive care in Los Angeles. "We have to wait and be patient," he said. "We have so little information ourselves."
He added: "She's obviously a very tough girl who's survived many things. I encourage everyone to pray for her."
Fisher had been on tour promoting her latest book, The Princess Diarist.
The heart attack happened about 15 minutes before the plane landed in LA, celebrity news website TMZ reported. A medic who was travelling on the plane administered CPR.
Paramedics then spent a further 15 minutes administering more CPR to Fisher before getting a pulse, TMZ said. The actress was on a ventilator in the UCLA medical centre, the website said.
A law enforcement official told NBC that her condition was "not good".
Passengers on the plane have been tweeting about what they saw.
Fisher appeared in the original Star Wars trilogy and Star Wars: The Force Awakens, a sequel released last year.
She was in other films including The Blues Brothers and When Harry Met Sally.
She has written four novels and three memoirs and was previously married to the musician Paul Simon.
She is the daughter of singer Eddie Fisher and actress Debbie Reynolds.
India finished the opening day of the final Test against South Africa on 231-7 - the highest score of the series.
[NEXT_CONCEPT]
Two road workers have been seriously hurt in an accident involving a van in mid Devon.
[NEXT_CONCEPT]
Friends, family and colleagues have sent best wishes to the actress Carrie Fisher, who is in intensive care after suffering a heart attack during a flight, her brother says.