After easily winning the first two games by seven wickets and then 10 wickets when batting second, for most of the New Zealanders it was their first turn to bat after they won the toss for the first time and made Sri Lanka bowl.
Williamson, deputising as captain in place of the injured Brendon McCullum, notched his 22nd ODI half-century while Tom Latham was the next highest scorer with 42 at Nelson's oval.
By the end of the innings the average stood at 5.54, helped by Mitchell Santner's 38 and Tim Southee's 18 off four balls in the last over.
After being humbled in the first two games, Sri Lanka fought their way into the third match through the inexperienced Jeffrey Vandersay and Dumantha Chameera.
In one over Vandersay claimed Tom Latham for 42 and Ross Taylor without scoring to give the 25-year-old leg-spinner his first wickets in his second international.
Chameera, 23, in his seventh ODI, claimed Martin Guptill and Henry Nicholls, caught Williamson and ran out Santner.
When Williamson cracked three fours off consecutive balls from Angelo Mathews in the 14th over, the Sri Lankan captain turned to spin with quick results.
Latham scooped Vandersay to give Nuwan Pradeep a simple catch at backward square-leg and Taylor was caught at slip off the second ball he faced.
Henry Nicholls was bowled by Chameera for 20 while Williamson who was dropped on 30, was eventually undone by a full toss from Milinda Siriwardana which he slapped to Chameera at mid-on.
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