Jamieson wasn't required this morning but did his damage yesterday, taking 5-34 off 13 edge-of-the-seat overs.
The first two New Zealanders to achieve the feat were Jack Cowie and Tom Burtt in the first test of the famous 1949 tour to England, where all the tests were drawn.
Cowie took 5-127 and left-arm spinner Burtt 5-97.
Thirty-five years later Sir Richard Hadlee and Ewen Chatfield repeated the feat when New Zealand beat Sri Lanka in the third test at Colombo.
Hadlee took 5-73 and the metronomic Chatfield 5-63.
Southee and Jamieson, who led the team from the field at the end of the innings, join this rare club.
At lunch the West Indies were 73-2 with Boult taking the wickets of Kraigg Brathwaite and Darren Bravo.