New Zealand, who are 1-0 up in the three-Test series, were 334 for one at stumps with Conway on 178 having hit 25 fours.
West Indies, who trail 1-0 in the three-Test series, finished the day on 43 for no loss, still 419 behind their improbable target. Brandon King was batting on 37, while John Campbell was on two.
Rachin Ravindra smashed 176, while skipper Tom Latham ended his three-year wait for a Test hundred as the New Zealanders combined for a 279-run stand to effectively bat West Indies out of the opening test at Christchurch's Hagley Oval on Thursday.
He is the 10th batter to achieve a double of a double ton and century in a single Test match.
West Indies pace puts New Zealand on the ropes in Christchurch
Opener Devon Conway and debutant Mitchell Hay struck half-centuries to earn New Zealand a handy first-innings lead of 73 before their depleted bowling attack reduced West Indies to 32 for two to take control of the second Test in Wellington on Thursday.
Even as the focus remains on the T20 World Cup which is less than a month away, Kohli and Rohit will hog the limelight in the three ODIs over the next seven days.
New Zealand captain Michael Bracewell on Tuesday said it would be "silly to underestimate" Indian batting superstars Virat Kohli and Rohit Sharma, and backed the stalwarts to play next year's ODI World Cup.
Fast bowler Jacob Duffy and spinner Ajaz Patel routed West Indies as New Zealand won the third and final Test by 323 runs to complete a 2-0 series victory
New Zealand stumper-batsman Tom Latham was ruled out of the one-day series against Pakistan with a hand leaving Michael Bracewell to continue as the side's captain.
Kane Williamson is unavailable for ODI selection due to his commitments in the SA20 league.
India on Friday slipped a rung to sixth position on the World Test Championship standings after New Zealand's comprehensive nine-wicket victory against the West Indies in Wellington.
Ravindra, Conway pave the way as New Zealand clinch ODI series against West Indies
Young blocked the first ball of the Abrar Ahmed over for a dot before sweeping the ball to square leg to bring up his century.
New Zealand dismissed West Indies for 205 and reached 24 without loss in reply on the opening day of the second Test on Wednesday.
New Zealand batsman Tom Latham says his team will take confidence from their recent win over South Africa in the tri-series when they face the same opponents in the semifinal of the Champions Trophy in Lahore on Wednesday.
Seamer Jacob Duffy claimed a maiden five-wicket haul to secure New Zealand a handy first innings lead and the upper hand in the opening Test against West Indies.
Justin Greaves produced a nine-and-a-half-hour batting masterclass before walking into Caribbean lore after his maiden Test double hundred secured an unlikely draw for West Indies.
Justin Greaves struck an epic unbeaten 202 against a depleted New Zealand attack to help the West Indies snatch a memorable draw in the opening Test at Christchurch's Hagley Oval on Saturday.
Kane Williamson was included in the New Zealand squad for December's three-Test series against West Indies.
Former New Zealand captain Kane Williamson has said he hopes to continue playing until the 2027 World Cup as he prepares to make his return for his country in the three-match One-Day International series against England, which starts on Sunday.
Latham emphasised the importance of putting up runs early in the innings, recognising it as the foundation for New Zealand's success.
Daryl Mitchell's runs had steered the hosts to their victories in Tauranga and Hamilton and when he departed for 44 to leave his team still 27 runs from their target on 196-8, the English scented an unlikely victory.
Kane Williamson has decided to skip the three-match ODI series to focus on the Test series against the West Indies next month.
The United States authorities have arrested an Indian-American government employee on charges of 'grand larceny' for allegedly working a 'second, full-time job' during the hours he was being paid to perform his official duties as a state employee.
'It's obviously a great challenge that's ahead and I guess it's something to look forward to.'
Blair Tickner took 4/34 and Daryl Mitchell hit 56 not out as New Zealand beat England by five wickets in the second one-day international in Hamilton on Wednesday to seal the three-match series 2-0.
Even though India's all-round struggles in the ongoing series have compounded their issues, there were some soothing words from the opposition camp, which has not put a foot wrong on this trip.
Tom Latham and Kane Williamson led New Zealand's fightback with sparkling half-centuries as the Black Caps reached 255-4 on the rain-hit second day of their opening Test against Sri Lanka in Galle
The presence of a host of experienced batters and bowlers, Latham said, makes India a formidable opponent.
New Zealand have yet to decide on a replacement for Williamson for the white-ball roles but Latham's record in T20s may count against him if selectors opt for a single captain for both the short-format teams.
Devon Conway, Henry Nicholls, and Rachin Ravindra all scored 150 and over as New Zealand built up a commanding 476-run lead against hosts Zimbabwe at the end of the second day of the second Test at the Queens Sports Club in Bulawayo on Friday.
New Zealand beat Zimbabwe by nine wickets to win first Test
New Zealand clinched the tri-nation title by beating hosts Pakistan by five wickets in the final in Karachi on Friday to give them a major boost ahead of next week's Champions Trophy.
New Zealand captain Mitchell Santner praised centurions Will Young and Tom Latham for their crucial contributions in the team's emphatic 60-run victory over Pakistan in the Champions Trophy opener.
IMAGES from the Champions Trophy Group A match played between Pakistan and New Zealand at the National Stadium in Karachi on Wednesday.
The result meant that defending champions Pakistan joined Bangladesh in being knocked out of the tournament after losing their opening two matches against New Zealand and India.
Tom Latham broke the 24-year-old record of Sachin Tendulkar of the highest ODI score made on a birthday
New Zealand called up two local left-arm wrist spinners to bowl to left-handers Tom Latham and Michael Bracewell at their nets in Dubai on Saturday.
Pakistan were all out for 260 in 47.2 overs with Babar Azam (64) and Khushdil Shah (69) scoring half-centuries but the hosts never looked in the hunt.
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