The huge knock has seen the hosts extend their first innings lead over the visitors.
New Zealand went to lunch 403/3 on day three in Wellington, 121 runs in front of the tourists.
The Black Caps captain began the 2018/19 season with 91 from 93 balls against Sri Lanka yesterday, while Latham hit an unbeaten 121.
Aaron Finch had to retire hurt after this shocker against India.
India's captain helped his side out of hole with a classy ton,
New Zealand reached stumps at 311-2 in reply to Sri Lanka's first innings of 282.
Latham was 57 not out, Williamson 71 not out and New Zealand was 175-1 at the break.
New Zealand finished the morning session at 59/1, 223 runs behind the tourists in Wellington.
The Indian skipper was 82 not out, as his side trail by 154 runs in the first innings.
Tim Southee took 5-67 as New Zealand exploited an influential toss to contain Sri Lanka to 275-9 on day one of the first Test in Wellington.
Sri Lanka finished day one of the first Test with 275-9 against the Black Caps at the Basin Reserve, Wellington.
The tourists fought back to reach 73/3 at lunch on day one at the Basin Reserve.
NZ will play a two-Test home series against a Sri Lanka team in disarray.
Including Ajaz Patel will give NZ the best chance of beating Sri Lanka.
Tim Southee admitted it would be nice recognition for team's form over a number of years.
Watson is aware his time in the game is winding down and since his retirement from international cricket in 2016, he has eked out a living travelling the world as a T20 gun for hire.
346 cricketers are shortlisted in this year's auction which takes place on Devember 18.
Akila Dananjaya has been suspended by the ICC for exceeding the 15 degrees level of tolerance.
Kim McConnie, the head of the league, says the change "reflects what BBL is about."
The pair helped NZ to a series win over Pakistan last week.
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Tim Paine and Nathan Lyon have fired shots at the Decision Review System after their 31-run loss to India.
The Brisbane Heat have made the change as part of a master plan, coach Dan Vettori said.
Gary Stead named a 13-man squad for Saturday's first Test in Wellington.
The Black Caps will face Sri Lanka in two Tests in Wellington and Christchurch starting this weekend.
Australia, set an imposing target of 323, reached 4-104 at stumps.
Will Somerville, Ajaz Patel and Ish Sodhi are vying to play in Wellington.
The hosts need 323 to take a 1-0 series lead in Adelaide.
Gary Stead's first tour in charge of the Black Caps saw a famous win over Pakistan.
Gary Stead has five spin options to chose from when the Black Caps face Sri Lanka next week.
The tourists boasted a 166-run lead at stumps on Saturday, having reached 3-151 in their second innings.
