New Zealand ended the day at a healthy 329/4 with McCullum still unbeaten on 143. Corey Anderson was keeping him company on 42.
Zaheer Khan and Ishant Sharma took two wickets apiece for India.
Williamson and McCullum were involved in a double century stand for the fourth wicket after coming together at 30/3.
Both were in a punishing mood as the Indian attack wilted after a promising beginning.
Image: New Zealand’s Brendon McCullum celebrates his century against India on the first day of the first cricket test at Eden Park in Auckland, New Zealand, Thursday, Feb. 6, 2014.