Williamson was awarded the man of the match for his century.
Latham, who hit 6 fours and a six, played aggressive cricket to thwart the Indian spin and pace attack during his run-a-ball 46.
New Zealand defeated India by six runs in a closely-fought second One-Day International (ODI) cricket match at the Ferozeshah Kotla here on Thursday - the Kiwis' first win on the current tour of the country.
Williamson struck a wonderful 118 (128b, 14x4, 1x6) for New Zealand, but once the captain was dismissed, the Kiwis lost their way completely, eventually only managing 242 for nine in their 50 overs, when a score near 300, at one point, looked likely. Ajinkya Rahane took 49 balls for his 28 while Mahendra Singh Dhoni took 65 balls for his 39.
Hardik Pandya (36) and Umesh Yadav (18) had tried their best with a 49-run stand for the ninth wicket but Pandyas dismissal in the penultimate over ended Indias hopes with Southee cleaning up Jasprit Bumrah (0) in the final over with a flawless yorker.
Chasing a modest 243, India were skittled out for 236 by a disciplined Kiwi bowling and an inspired fielding effort from the visitors. India chase began on a poor note when Rohit Sharma (15) edged one to the keeper with score reading 20 for one.
Left-arm spinner Mitchell Santner got the big wicket of Virat Kohli (9) with wicketkeeper Luke Ronchi taking a great reflex catch down the leg side. Latham, as he did in the first ODI, is playing another fine innings. The decision appeared controversial as replays suggested that the ball might have bounced before Corey Anderson caught it.
On Tuesday, Raina spent a long time at the nets raising hopes of the middle-order batsman making a comeback for the Thursday's encounter at the Kotla.
At the face of it, there is apparently no danger to Dhoni's captaincy since the team is still winning matches. Now Dhoni would like to ideally win the series 5-0 against a New Zealand side.
Just as Jadhav seemed well set, he tickled an edge back to the 'keeper and was out to Henry.
Southee ended Dhonis misery with a stunning one handed return catch when the Indian skipper failed to read a slower one.
"It was nice that he really bowled well in his first game with the new ball".
Umesh Yadav (1/42) started with a flawless delivery that pitched on the middle and knocked off Martin Guptill's (0) as off-stump. In the first ODI, he batted with supreme confidence before getting run out. Williamson looked unaffected by the early setback who came in at No. 3 and was looking set from the very beginning.
Rohit's departure brought in local boy Virat Kohli (9) - a moment which the capacity crowd at Kotla waited for all day - amidst thunderous applause. He has shown over the years that he has enough capabilities as a batsman.
Williamson and Latham put on a 120-run partnership before the two were finally separated. The breakthrough came from an unlikely source - Jadhav, trapping the latter lbw.