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ND were faced with a modest chase of 194 for victory on day four and Williamson made 121 from 142 balls in just under three hours. His knock included 11 fours and a pair of sixes.
It was the 22-year-old's 12th first-class century and he found able support from James Marshall who was not out on 36 when the winning runs were struck.
Earlier in the day, Luke Ronchi made his second century of the match as Wellington reached 390 in their second innings after being forced to follow on.
Ronchi, who becomes eligible to represent New Zealand next month after representing Australia, followed up his first-innings score of 113 with 108 and also pouched eight catches, six in ND's first innings.
The in-form Scott Kuggeleijn also continued his recent spark with the bat as he smacked 83 from No 8 for Wellington and ND leg-spinner Ish Sodhi snagged career-best figures of 5-128.
The win was the first of the Plunket Shield campaign for ND who still remain at the foot of the ladder.
In Dunedin, Otago and Central Districts wrapped their game up at tea on day four as it laboured to an uneventful draw.
Trailing by 22 runs on the first innings Otago went about their business on the final day of play as they batted CD out of the game and ensured they wouldn't lose as they crawled to 227-4 then declared at tea, which ended the contest.
Night watchman Neil Wagner top-scored with 65, while import Ryan ten Doeschate followed-up his first-innings hundred with an unbeaten 54 in his 100th first-class match.
Part-time leg-spinner Jeet Raval grabbed two wickets for CD who maintained their spot at the top of the Plunket Shield.
The Plunket Shield goes on hiatus for a month now as the domestic Twenty20 competition gets in to full swing during the holiday season.