In all Test cricket, Atkinson’s is the first hat-trick since South Africa spinner Keshav Maharaj against West Indies in 2021.
Atkinson’s three wickets in three balls is also the first hat-trick taken at the historic Basin Reserve.
New Zealand resumed on 86-5, 194 adrift. Brydon Carse needed only 10 balls of his spell to take Tom Blundell’s off stump and, in the same over, nightwatchman Will O’Rourke was plumb lbw.
Smith and Glenn Phillips attempted a counter-attack, adding 29 in 27 balls, before Atkinson’s magic moment.
Smith was looking to leave, but extra bounce had the ball ricochet off his bat and down on to middle stump.
Number 10 Henry was defenceless against a brutal lifter and Southee, with the field set for a short ball, was hit in front by one Atkinson speared in.
Atkinson joins Moeen, Broad and 19th century spinner Johnny Briggs as the England players to achieve a Test century and a hat-trick.
Wasim Akram, Abdul Razzaq, Harbhajan Singh, James Franklin, Irfan Pathan and Sohan Gazi have also done such a double.