The Black Caps were on 229-4 when rain caused the day to come to a premature end, 171 runs ahead as they replied to the tourists’ 58.
Following rain breaks either side of an early tea, another shower interrupted the action in the evening, and, at a final inspection, it was decided no further play was possible.
Williamson had begun the day at Eden Park on 91 and completed a national-record 18th Test century.
The New Zealand captain moved one century above team-mate Ross Taylor and Kiwi great Martin Crowe when he reached three figures, this time from 196 balls.
Williamson and Henry Nicholls kept the hosts in control of this opening day-night Test as they took their unbroken stand to 75 and the total to 197-3 in reply to England’s miserable 58 all out.
After a rain break either side of an early tea, James Anderson (3-53) saw off Williamson (102) lbw pushing forward to the second new ball.
As another shower swept in to interrupt play again, though, Nicholls was within a single of a painstaking 50.
Half-centuries from Natalie Sciver and Tammy Beaumont in Mumbai boosted England to an eight-wicket victory over Australia in the women’s T20 Tri-Series.
England restricted Australia to 149-8, despite Australia captain Rachael Haynes top-scoring with 65, as Jenny Gunn plundered three wickets. Sciver took two and Danielle Hazell one.
Sciver’s 68 contained 12 boundaries, with Beaumont also finishing unbeaten as she registered eight fours in her 58 at the Brabourne Stadium.
Bryony Smith, who made a half-century in a warm-up match against India A this week, was dismissed for a single on her England debut and left-arm pace bowler Katie George also made her bow.