The Black Caps honoured former Herald chief sports writer David Leggat, who passed away last week, by wearing black armbands and in Leggo parlance, players would have had plenty of time for a graze (food) or some bobos (sleep) during the two-hour delay.
Shortly after the retutn, Phillips fell for 17 before Williamson and Daryl Mitchell put on 46 for the fourth wicket.
Mitchell hit one towering six down the ground off Obed McCoy before a faint edge the next ball for 16.
Williamson was then caught in the deep by Hayden Walsh Jr for 47 off 33 balls to give Smith his third wicket. Jimmy Neesham's 33 off 15 ensured the Black Caps set a strong total of 185 for five.
In their chase, regular wickets halted the West Indians with Shamarh Brooks (42 off 43) the only batsman in the top five hanging around longer than nine deliveries, although skipper Nicholas Pooran did briefly entertain with three boundaries in his eight ball stay.
Mitchell Santner (3-19) led the way for the tourists including the key dismissals of Brooks and Pooran while Boult, Southee, Lockie Ferguson and Ish Sodhi all took a wicket each.
Late hitting from Romario Shepherd (31 from 16) and Smith (27 off 12) at least made the defeat a more respectable margin.