The win had been set up the night before when the Black Caps bowled out the tourists for 103 in their second innings, but Williamson (56) and Hamish Rutherford (48no) ensured there were no nerves with a stand of 83 for the second wicket.
The win, which arrived after lunch, wrapped up a 2-0 win in the three-match series for Brendon McCullum's men.
Having seen out two overs the previous night without alarm, New Zealand had a moment of discomfort when Peter Fulton was caught and bowled by West Indies captain Darren Sammy for 10.
Four maidens followed as the Windies piled on the pressure, before Rutherford broke the shackles by cutting Sunil Narine for four.
Thereafter it was plain sailing for New Zealand, and Williamson, who took 15 balls to get off the mark, sped past his partner with a couple of boundaries off Narine.
The Black Caps could not quite get the job done before lunch, but Williamson passed 50 after the resumption.
He fell moments before the victory was sealed when a Veerasammy Permaul delivery kept low, but Rutherford drove Narsingh Deonarine for four to end it.