Latham has now scored five centuries in the last 10 Test innings but preferred to talk about "a reasonably good day" for New Zealand rather than focus on himself.
Stokes came into the match with a knee injury and was in pain as he bowled only two overs in the first two sessions.
And he disclosed he will never tire of attempting to improve his batting and appeared unconcerned by question marks again raised about his captaincy after a passive England display in the first Test.More news: Rep. Nunes sues CNN for $435 million over Ukraine story
But from two for 39, Latham and Taylor put on 116 for the third wicket when Taylor went for 53 to have New Zealand three for 155.
The worrying thing for Root and new coach Chris Silverwood, who will leave the tour on Saturday after a family bereavement, is that Root has been on a downward track since he succeeded Alastair Cook as skipper nearly three years ago. "He felt some discomfort at the end of his second over".
The second and final Test starts on Friday but Root, who reported no issues among his side after 201 overs in the field during New Zealand's titanic innings last week, is unfazed by the tight turnaround.
New Zealand were also waiting for a late pitch inspection before deciding whether Matt Henry or Lockie Ferguson would replace Trent Boult, who strained a rib muscle in the first Test. Ferguson, like England's Archer, is a 150 kilometres (93 miles) per hour plus express bowler, while Henry was noted for his swing ability with the new ball and took five wickets against South Africa in Hamilton two years ago.More news: China wants tariff rollback for phase 1 trade deal
A relieved Taylor batted on to bring up his 32nd Test half-century with a four off Chris Woakes but was out next ball, caught at first slip by Joe Root.
Latham used placement and timing to find boundaries through midwicket and reached his century with an on-drive from the second ball of the only over bowled by Root, England's part-time off-spinner.
Taylor, on 25, successfully challenged an lbw decision which went in favor of Broad and replays showed the faintest of inside edges.
Kiwis bowling coach Shane Jurgensen said: "It's a really fantastic opportunity for Daryl if he's selected. He has dealt with it very well; he'll be absolutely fine to play", Root said.More news: Qualcomm's Snapdragon 865 is Next Year's Big Processor
There was expected to be assistance for pacers with both the captains admitting that they would've preferred to bowl, but it didn't pan out likewise. "He's a big player for them and it's important we try to get him out early in the morning".
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