At tea, the West Indies were 399-6, requiring a further 132 runs with four wickets remaining if they are to achieve a historic victory.

Greaves was not out 157, and Kemar Roach 50, the highest test score for both.

Set a colossal target of 531, 113 more than the current record for a successful fourth-innings run chase, the West Indies were in dire straits at 72-4.

But New Zealand were struggling with injuries to Matt Henry and Nathan Smith, reducing their pace attack to just Jacob Duffy and Zak Foulkes.

Both are playing only their second test.

The flat wicket also offered little help to the spinners as Greaves and Hope turned the West Indies innings around with a 196-run stand for the fifth wicket.

When Hope went for 140, and Tevin Imlach followed for four, the West Indies were 277-6.

Duffy took Hope's wicket courtesy of a stunning leg-side catch by wicketkeeper Tom Latha, and Imlach was trapped lbw by Foulkes.

Roach and Greaves have put on 122 for the seventh wicket.

Roach was dropped on 30 and 47 and survived an attempted run-out when the throw went wide of the stumps.

Duffy has taken 3-97 for New Zealand to go with his five wickets in the first innings.

NEW ZEALAND: Tom Latham (capt), Devon Conway, Kane Williamson, Rachin Ravindra, Will Young, Tom Blundell, Michael Bracewell, Zak Foulkes, Nathan Smith, Matt Henry, Jacob Duffy.

WEST INDIES: John Campbell, Tagenarine Chanderpaul, Alick Athanaze, Shai Hope, Roston Chase (capt), Justin Greaves, Tevin Imlach, Kemar Roach, Johan Layne, Jayden Seales, Ojay Shields