New Zealand closed on 315 for four in reply to Zimbabwe’s first-innings 164. Ross Taylor (38) and nightwatchman Ish Sodhi (5) were not out at the close.
Latham reached his fourth test century soon after tea before being caught by stand-in wicketkeeper Brian Chairi off the part-time bowling of veteran Hamilton Masakadza for 105 from 209 balls.
Latham and Williamson compiled a second-wicket partnership of 156. Williamson fell nine runs short of his century after a sharp catch at slip by Masakadza off the leg-spin bowling of home skipper Graeme Cremer.
The New Zealand captain had benefited from a contentious decision from the television umpire when he looked to have been caught at first slip by Sikandar Raza off Cremer when he was on 72.
Williamson asked Raza to confirm he had taken the catch and despite a positive response he spoke to the umpires who opted to get television evidence which could not prove the dismissal.
Opener Martin Guptill was dismissed in the first session for 40, was caught in the gully to hand debutant Chamu Chibhabha a first test wicket.
Henry Nicholls was the fourth wicket to fall, caught behind by Chairi from a full delivery by Donald Tiripano.
Chairi was deputising for Regis Chakabva who was confined to bed on Friday with a high temperature.
The New Zealanders will look to bat through the third day after Williamson said his side would seek time at the crease to prepare for tougher series in South Africa and India over the next two months.
(Reporting by Mark Gleeson in Cape Town; Editing by Ed Osmond)
