India were 19 for 0 at stumps and needed another 87 runs to win the final Test to reclaim Border-Gavaskar Trophy.
Williamson equalled the Kiwis record for test centuries as his side reached 321 for four at the close of day three of the third test against South Africa in Hamilton on Monday.
Pakistan took a six-wicket victory over West Indies in Barbados on Sunday in the first of four Twenty20 internationals.
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.