Published: 2021-06-05 19:29:01 BdST
Opener Rory Burns was unbeaten on 72 with debutant Ollie Robinson at the other end on 16 at the break.
England had resumed their first innings on 111-2 after rain washed out day three, and Jamieson gave New Zealand the perfect start when he dismissed Joe Root with the first delivery of the day.
He forced the England skipper into a defensive shot, and the ball flew off a thick outside edge into the hands of Ross Taylor in the slips.
Ollie Pope (22) was the next to go after a solid start, missing an angled delivery from Southee which rapped him on the pads. The umpire demurred, but New Zealand successfully reviewed and overturned the decision.
Southee then dismissed Dan Lawrence and James Bracey in quick succession with both batsmen returning to the pavilion for ducks.
Lawrence played a loose drive to nick the ball to Colin de Grandhomme at third slip while Bracey, on his Test debut, saw his off stump uprooted.
New Zealand posted a first innings total of 378, with debutant Devon Conway scoring a double ton.