Facing a daunting target of 531—113 more than the record for a successful fourth-innings chase—the West Indies finished the match at 457-6, marking the second-highest total in a Test fourth innings, News.Az reports, citing AFP.
Greaves batted for nearly 10 hours, facing 388 balls to achieve his maiden double century in the penultimate over of the match.
Roach, who remained unbeaten on a career-best 58, played a crucial role in the survival effort, facing 72 dot balls when he was on 53.
Together, the pair formed a resolute 180-run partnership for the seventh wicket, ensuring the West Indies held on for a draw.
"Kemar, the senior pro, guided me all the way," said man-of-the-match Greaves.
"Coach told me once you get in, stay in. To be a part of history is exciting, but for me, it's one day at a time.
"For us, it was just about getting into the last session."
A draw seemed a distant prospect for the tourists when the top order failed to fire yet again and they slumped to 72-4.
But New Zealand were down on fire power as injuries to Matt Henry and Nathan Smith reduced their pace attack in the second innings to just Jacob Duffy and Zak Foulkes.
Both were playing only their second Test.
The placid pitch was also of little assistance to the spinners, allowing Shai Hope and Greaves to cash in for the fifth wicket amassing 196 runs in a 64-over stand.
The West Indies resumed the final day at 212-4 with a confident Hope and Greaves adding 23 in six overs of spin before blunting the new-ball attack for more than 12 overs, before Hope was dismissed for 140.
A short ball from Duffy outside the leg stump tempted Hope to hook but the ball climbed, grazed the glove and a diving Tom Latham took a stunning one-handed catch to complete the dismissal.
Tevin Imlach came and went quickly, lbw to Foulkes for four, and New Zealand felt the initiative had swung their way again with the West Indies 277-6.
But when Roach joined Greaves the pendulum swung back the other way as West Indies reached 399-6 at tea, needing a further 132 with four wickets remaining if they were to achieve a historic victory in the final session.
Luck was with Roach, who received five lives.
He was dropped on 30 and 47 and survived a run-out when the throw went wide of the stumps.
He was given not out to an lbw appeal and again for a caught behind, both off Michael Bracewell, when television replays showed he was out both times.
Duffy was New Zealand's most successful bowler with 3-122 to go with his five wickets in the first Test.
The second Test starts in Wellington on Wednesday.
