A KL Rahul century was not enough of a platform for the tourists, who made 296 for seven after being put in to bat.
However, it was Colin de Grandhomme (58*) and Latham (32*) who guided the Blackcaps to victory in the end by five wickets with 17 balls to spare.
In their pursuit of clinching a consolidated win against the hosts, India locked horns with New Zealand in the final ODI of the three-match series.
Williamson hurt his shoulder while fielding in the third Twenty20 game against India and he missed the final two matches of that series as well. Haven't played so badly, but we didn't grab opportunities.
"It looks a hard surface with good grass on it and we want to put a total on the board, as I've spoken about in the past", he said.
Rahul was the second top-scorer for India in the three-match series with 88 not out, four and 112 to bring up 204 runs at an average of 102.
They played with lot more intensity than we did.
Missing key names such as Trent Boult, Lockie Ferguson and Matt Henry, the Black Caps' makeshift bowling attack restricted India to 251 all out, chasing New Zealand's perhaps under par score of 273/8. On Tuesday, he played yet another impressive knock, scoring a century in the third ODI against New Zealand although it went in vain.
His fourth wicket came when Shardul Thakur sent a full toss straight to de Grandhomme, and the bowler was unlucky not to get another when Navdeep Saini nearly edged the next delivery onto his stumps.
The match at Bay Oval in Mount Maunganui is the final limited overs game of the tour with the first of two Tests starting at Wellington's Basin Reserve on Feb 21.
"We have a really balanced Test team and we feel we can win the series here, but we need to step on to the park with the right kind of mindset".
The results of both matches will count toward the inaugural ICC World Test Championship, in which India are runaway leaders at the top of the ladder.
After the drubbing 2-0 defeat in the ODI series, Virat Kohli and his troops were hoping to finish their dismal campaign on a positive note.
"We know how good they are at all formats, but for us the clarity about the roles the guys had was the most important thing".