A day which began with so much promise soon turned into a grind in the field for the Black Caps in Christchurch.
England have batted themselves into a strong position at stumps on day two, courtesy of an unbeaten century by Harry Brook to trail by just 29 runs with five first innings wickets in hand.
Rubbing salt in, Latham dropped Brook on 41 at first slip when he nicked one behind from Smith and again on 70, when he skied one from Phillips to Conway in the deep, but the opener spilled the opportunity to break the stand.
Debutant Nathan Smith claimed two early wickets, including Joe Root for a duck, while Glen Phillips added to his half century with a catch for the ages at gully.
Starting the day at 319 for eight, the Black Caps added a further 29 runs before Will O'Rourke lost his middle stump to Brydon Carse, with Phillips finishing unbeaten on 58, as the Kiwis posted 348.
Carse took 4-64 with spinner Shoaib Bashir claiming 4-69.
The Kiwis didn't take long to inflict further damage with the ball, taking early scalps to have the tourists reeling at 45 for three at lunch, Smith removing both Joe Root for naught and Jacob Bethell.
Zac Crawley fell for a 12-ball duck to Matt Henry, while O'Rourke sent Ben Duckett back to the sheds for 46.
Harry Brook and Oli Pope then steadied the ship, with both men bringing up their half centuries just before tea, before a piece of Phillips magic.
The crucial scalp came as Philips launched himself through the air and plucked a powerful cut shot by Pope out of the sky. With Pope gone for 77, the partnership came to an end for 151 runs, as Southee took his first wicket of the test.
Then entered Ben Stokes, who piled on more runs with Brook, as the two finished unbeaten on 132 and 37, as England ended at 319/5.
Play will resume on Saturday at 11am.
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