India were reeling at 66-3 and then at 139-6 but Rahane, often unnoticed in the crowd of flashy strokeplayers around him, featured in two fifty-plus stands to help India post the highest total in the low-scoring four-match series.
Ravichandran Ashwin was giving him company on six at stumps.
For South Africa, Piedt claimed four wickets while paceman Kyle Abbot (3-23) also justified his recall for the final test against India, who have taken an unassailable 2-0 lead.
"I think the game is still even, if we strike with the new ball tomorrow morning, under-250 should be a good enough score," Piedt told reporters.
"It (pitch) is two-paced, the odd one is skidding and bouncing as well. It's been a good wicket for everyone today."
Of all the tracks used in the four-match series, the hard 22-yard strip at the Ferozeshah Kotla stadium offered the least turn but Piedt conjured up a performance that left many wondering why the 25-year-old was not played before.
Home captain Virat Kohli won his fourth successive toss in the series and opted to bat on a track which wore cracks but looked hard, unlike the rank turners used in previous tests.
Morne Morkel and Abbott bowled with a lot of discipline, allowing only 14 runs in the first 10 overs but it was Piedt who drew first blood by dismissing opener Murali Vijay (12).
The spinner also struck early in the second session, trapping the set Shikhar Dhawan (33) leg before while Abbott bowled out Cheteshwar Pujara (14) in the next over to peg back the hosts.
Kohli (44) and Rahane did not look perturbed though, and boundaries started flowing as they negated the South African bowlers with consummate ease.
The duo had raised 70 runs in 17 overs when Kohli fell to Piedt, sweeping the spinner straight into the body of Temba Bavuma at short leg.
The ball ballooned up after hitting the evading fielder on his thigh and wicketkeeper Dane Vilas sprinted from behind the stumps before diving full stretch to take the catch.
Rohit Sharma got a reprieve when Amla dropped him at slip but the batsman could not add to that scratchy single and hoicked the first ball of the next over from Piedt to Imran Tahir at long on.
Abbott breached Wriddhiman Saha's defence at the stroke of tea but Rahane and Ravindra Jadeja (24) added 59 runs for the seventh wicket to take India close to the 200-run mark.
Abbott dismissed Jadeja for his third wicket but Rahane stood firm after a cultured 155-ball knock that included nine boundaries and two sixes.
"If we can bat one more session tomorrow morning, I think it would be a good effort," India batting coach Sanjay Bangar told reporters.
"The lower order has contributed regularly, which used to be an issue in the past. The way they have batted in Sri Lanka and also in this series, it's a positive for us."
(Editing by Sudipto Ganguly)
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