On a flat Basin Reserve wicket in Wellington, New Zealand were 445 for five with Williamson and Watling's unbroken sixth-wicket stand worth 286.
Sri Lanka need a victory to draw the two-Test series but their chances were fading as the Williamson-Watling partnership continued.
Williamson, not out 190, was gathering runs steadily at one end while Watling maintained an impenetrable defence at the other to be 118.
In two sessions, since resuming on the fourth day with New Zealand on 253-5, Williamson has added 110 to his overnight 80 while the more circumspect Watling has extended his overnight 48 by 70 runs.
Rangana Herath, the most successful wicket taker in the world last year, induced a chance from Williamson who gloved a turning ball on 104 but wicketkeeper Prasanna Jayawardene was unable to take the catch.
It was a rare opportunity for Sri Lanka as captain Angelo Mathews set defensive fields waiting for a mistake by the batsmen and when they had the chance it was lost.
Williamson, dropped earlier on 29 and 60 was just short of his Test high 192, and has now posted nine centuries to move up to sixth equal with Stephen Fleming on the all-time list of New Zealand century makers.
Then, as now, New Zealand led 1-0 going into the Test and needed to avoid defeat to claim the series.
A win or draw against Sri Lanka will give New Zealand a third consecutive home series win.
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