The visitors were strongly placed at 152-1 following a 91-run stand for the second wicket between skipper Graeme Smith and Hashim Amla before slipping to 175-4 at tea on the opening day.
Ashwell Prince (10) and AB de Villiers (three) were the not out batsmen at the break.
Off-spinner Harbhajan Singh, paceman Ishant Sharma and part-time spinner Yuvraj Singh were the wicket-takers in the second session after the visitors had elected to bat.
Smith (69) gave his team a solid start with a 61-run stand for the opening wicket with Neil McKenzie (36) and then consolidated with Amla (51) before India struck on a turning track.
The visitors lead 1-0 in the series following their emphatic victory by an innings and 90 runs in the second Test in Ahmedabad. The opening match ended in a draw in Chennai.
India suffered a setback when they lost skipper and ace leg-spinner Anil Kumble to a groin injury before the match, wicket-keeper Mahendra Singh Dhoni leading the side for the first time in a Test.
With the pitch offering little assistance to fast bowlers, Dhoni introduced Harbhajan as early as the ninth over but had to wait for the first wicket.
Leg-spinner Piyush Chawla, a 19-year-old playing his first Test in two years, provided the breakthrough in his opening over when he had McKenzie stumped in the morning.
McKenzie had been looking solid during his 57-ball knock before losing his patience. He stepped out to drive the leg-spinner but was beaten by the flight, with Dhoni completing an easy stumping.
Smith continued to score comfortably, reaching his half-century with a six off Chawla and then hoisting Yuvraj for a second six in his 134-ball knock.
The South African captain fell immediately after hitting his second six, caught off his gloves by short-leg fielder Wasim Jaffer, who dived forward to bring off a low catch. Smith also hit eight fours.
Dhoni put his faith in spin on a pitch that helped slow bowlers, pressing part-timers Virender Sehwag and Yuvraj into the attack.
The stand-in captain kept spinners on from one end but turned to pace for a brief spell in the afternoon session.
The move paid off as Sharma breached Amla's defence for his first wicket. Then Harbhajan bowled Jacques Kallis for one to reduce the tourists to 161-4.
India's short-leg fielder Sourav Ganguly left the field after being struck on the back of his helmet off a shot from Amla.
India made three changes from the side that lost the second Test as they included fit-again Ishant, Chawla and middle-order batsman Yuvraj.