An inspired spell of spin bowling from Nathan Lyon pickup four wickets in final session and reduce India to 248-6 at stumps on second day.
A solid start from New Zealand to finish the day on a high and snatch the advantage even, after de Kock had rallied along with the lower order to take South Africa to 314.
Home side looks to make amends after 3-0 T20I series defeat at hands of Pakistan in UAE last September.
Sri Lanka were bowled out for 234 after Tamim scored a brilliant century to give Bangladesh 1-0 lead.
The chinaman bowler returned figures of 4 for 68, while Smith compiled a century as Australia were bundled out for 300.
South Africa were 123 for four at stumps on a rain-shortened first day of the third Test against New Zealand in Hamilton on Saturday.
Afghanistan clinch a 3-2 one-day series win over Ireland as Rahmat Shah scores century helps secure a seven-wicket victory at Greater Noida.
After success in Tests the Bangladesh look to tame host in One-day international too.
Australian No.2 spot remains in danger as they might drop a place if they lost to India and South Africa beat New Zealand at Hamilton.
Quinton de Kock fit to play in deciding third Test, but New Zealand will be without Boult, Southee and Taylor.