The slow left-armer, who had managed only six wickets in his previous 17 Tests, helped dismiss India after tea despite the home side winning the toss.
Murali Vijay top-scored with 75, while leg-spinner Imran Tahir claimed 2-23.
South Africa struggled to 28-2 in the 20 overs possible before the close, with opener Elgar unbeaten on 13.
Off-spinner Ravichandran Ashwin, opening the bowling, trapped Stiaan van Zyl lbw for five before Faf du Plessis - also playing no shot - was bowled by Ravindra Jadeja.
Nine of the 12 wickets in the day fell to spin, with Vijay - lbw attempting to sweep Simon Harmer - part of a collapse from 102-3.
"This is not a good Test pitch wicket though it's a result-oriented one," said Elgar. "We sort of expected it to play like that but we didn't expect it to crumble so early.
"It was right up there with the hardest ever Test cricket I've played. Let's hope that it backfires [on India] and turns out to be a great victory for us."
India's batting coach Sanjay Bangar responded: "It's a very challenging wicket where run-making is not easy.
"It says 201 runs on the scoreboard but it's worth far more. But I think runs can be made on this wicket as Vijay showed. It's going to be a test of patience both for batsmen and bowlers."
This Test is followed by matches in Bangalore, Nagpur and Delhi.
Part-time spinner Dean Elgar took 4-22 as South Africa bowled out India for 201 in Mohali, on the opening day of the four-Test series.