McCullum was on 71 with Williamson 79 not out, the pair enjoying an unbroken 149-run partnership.
Williamson's half-century was his sixth in succession against the tourists, having scored one in each of the five one day internationals that preceded the test series.
The 23-year-old Williamson was dropped on 32 by Murali Vijay at first slip off Mohammed Shami, and went on to bring up his half-century from 79 balls with a top-edge six that flew over captain and wicketkeeper Mahendra Singh Dhoni's head.
McCullum, who had initially accelerated the scoring after the break then slowed down, brought up his 29th test half century with a glorious off drive for his ninth boundary from a full-length Zaheer Khan delivery.
The pair scored 125 runs in 27 overs in the session as Dhoni became more defensive in his field placings, pushing fielders deeper and wider, which allowed New Zealand to keep the scoreboard ticking over with easy singles.
They had been thrust together with New Zealand on 30 for three after Dhoni had won his sixth successive toss on the tour and immediately asked the hosts to bat.
His three-pronged pace attack of Shami, Zaheer and Ishant Sharma exploited the green drop-in pitch and cool, overcast conditions to knock the top off New Zealand's batting and expose their middle order before the break.
Sharma had backed up the initial pressure applied by Shami, whose first six overs cost just five runs, with two wickets while Zaheer, who joined the test side to add some experience to their attack, had dismissed Peter Fulton for 13.
The tall Sharma had Hamish Rutherford well caught by a diving Ajinkya Rahane in the gully for six then had Ross Taylor caught by Ravindra Jadeja at wide mid-off for three.
Taylor's dimissal reduced the hosts to 30 for three before Williamson and McCullum consolidated, adding another 24 runs before lunch.
India's bowlers were unable to sustain their disciplined line and length after the lunch and were punished for bowling too short or too full.
(Reporting by Greg Stutchbury in Wellington; Editing by Ian Ransom)
