Latham and Williamson help New Zealand respond strongly to Sri Lanka
Latham excelled in good batting conditions after rain wiped out most of the morning session to score 70 off 111 balls, while Williamson took charge as the day wore on to make 55 off 104 balls and lay a solid platform.
Rachin Ravindra fell for a brisk 39 as Sri Lanka landed late blows to ease some of the pressure but Daryl Mitchell guided New Zealand to stumps making a solid 41 not out with Tom Blundell offering ample support on 18 not out.
Resuming on 302-7 after a battling 114 by Kamindu Mendis a day earlier, Sri Lanka lost momentum early in the morning as Ajaz Patel removed Prabath Jayasuriya for a duck before the first of two rain delays.
The hosts would add only three more runs to their overnight total as New Zealand pace bowler William O'Rourke returned after the interruption to take the final two wickets and finish with figures of 5-55.
Sri Lanka struggled to contain the flow of runs in sunny conditions after lunch as Latham cruised to his 29th Test half-century after Devon Conway was dismissed lbw by Ramesh Mendis against the run of play.
Latham departed at the stroke of tea just as New Zealand looked to build on their strong foundation, as the left-hander made a rare mistake while sweeping and was superbly caught by substitute Sadeera Samarawickrama off Jayasuriya.
Williamson shrugged off the end of their 73-run stand and forged another fine partnership with Ravindra en route to his own fifty but the former skipper top-edged a delivery from Dhananjaya de Silva to wicketkeeper Kusal Mendis.
Skipper De Silva struck again in his next over, bowling Ravindra after the batsman misjudged the line of the ball, to drag his team back into the match with the score at 196-4 but Sri Lanka were unable to make any more inroads.
