Sri Lanka were 20 for 3 at stumps on third day after New Zealand were bowled out for 578.
By the end of the third day, Australia had an overall lead of 175 runs with six wickets in hand.
Williamson masterclass and Latham special knock puts New Zealand in strong position against Sri Lanka in Wellington on Sunday.
Captain and vice captain led an Indian fightback on second day of the second Test against Australia at Perth on Saturday.
The paceman picked five-wicket haul to put New Zealand in a commanding position on the opening day of the first Test in Wellington on Saturday.
Century from Shai Hope but in Vain as Bangladesh clinch series 2-1.
Both Saifuddin and Mithun played their last T20I against Sri Lanka in February before being laid low by injuries and poor form.
Also returning to the side are fast bowlers Williams and Sheldon Cottrell; Pollard, Russell miss out.
Pitch comes alive to give India much-needed boost after Harris and Finch scores fifties
Fast bowlers give Sri Lanka hope against strong New Zealand in the first Test in Wellington on Saturday.
