The duo batted superbly to ensure the Black Caps end the day with a score of 243/2 in Hamilton.
The visitors opted to bowl first on a surface barely different from the look of the outfield, hoping to build inroads and give themselves an edge in the first innings.
Read Also: World Test Championship "extremely important" to West Indies, says coach Phil Simmons
However, Williamson (97*) and Latham (86) batted largely untroubled through their magnificent second-wicket stand of 154 runs as the Black Caps ended the proceedings with a score of 243/2.
Latham eventually got out bowled by pacer Kemar Roach (1/53) when he was looking set for a daddy hundred, but Williamson stood firm till the play was called, near his 22nd Test hundred in what has been an illustrious career.
After Latham, the great batsman found another able ally in middle-order stalwart Ross Taylor (31*), who himself will be eyeing a big score.
Earlier, debutant opener Will Young (5) got out cheaply LBW off the bowling of Shannon Gabriel (1/62).
Struggling to break through the Kiwi defense, the visiting attack resorted to keeping a tight line and length for much of the day.
Jason Holder (0/25) and Alzarri Joseph (0/43) were quite economical, but West Indies needed more wickets to have some grip of the contest.
New Zealand 243/2 in 78 overs (Kane Williamson 97* Tom Latham 86; Kemar Roach 1/53) versus West Indies on Day 1 of the first Test.