Latham and Nicholls put on 214 for the fourth wicket with Latham achieving his eighth century and Nicholls his fourth.
Sri Lanka enter the series against New Zealand on the back on a 3-0 series whitewash against England at home.
Williamson is one win away from becoming New Zealand’s second most successful Test captain.
Kaushal Silva and Malinda Pushpakumara have been dropped from a 17-man squad led by Dinesh Chandimal.
The SLC have named Danushka Gunathilaka, who has played five Tests, as replacement for the injured Chandimal.
Perera took four wickets and Pushpakumara three wickets to see off England in the final session of day one.
Dananjaya will undergo testing at an approved ICC centre within two weeks and he is expected to fly to Australia as soon as the second Test ends.
Sri Lanka face England in the next Test at Kandy which beings on November 14.
The second Test against England beginning on November 14 at the Pallekele International Cricket Stadium.
Herath who led both teams off the field in Galle on Friday as he ended his international career with 433 Test wickets to his name.