At break, South Africa were 80/1 with Graeme Smith batting on 31 and Hashim Amla on 11.
Earlier, South African skipper Graeme Smith won the toss and elected to bat on a pitch that is expected to assist spinners from day three.
India, who are playing without their injured batsman Sachin Tendulkar, suffered yet another blow as Kumble failed a late fitness test. His deputy MS Dhoni became the first wicketkeeper to captain India in a Test.
India went into the match with two pacemen and as many spinners on a pitch expected to favour slow bowlers, but there was little for the four-man attack in the morning session.
Left-handed Smith and McKenzie batted sensibly to ensure South Africa do not squander the advantage of batting first on a track lacking both pace and bounce.
Both waited patiently to punish loose deliveries, with McKenzie edging Sharma past third slip for four and then pulling the next delivery for a boundary early in the morning.
India pressed off-spinner Harbhajan Singh into the attack in the ninth over but it was Chawla who provided the breakthrough.
McKenzie fell immediately after driving Chawla for a four. He was beaten by the flight while stepping out to drive the spinner, with Dhoni completing an easy stumping.
While South Africa retained the same squad that played the second Test in Ahmedabad, India made three changes. RP Singh and Irfan Pathan made way for Ishant Sharma and Yuvraj Singh, the extra batsman.
Kumble's absence gave an opportunity for young leg-spinner Piyush Chalwa to play his first Test since his debut in March 2006.