Resuming on an overnight 178 not out, Conway carried New Zealand's first innings to a commanding declaration at 575/8. The left-hander reached his double century off 316 balls and went on to make a superb 227, his second Test double hundred.
His innings featured 28 boundaries and eclipsed Neil McKenzie's long-standing New Zealand Test best of 226. Conway's only previous double century had come on debut against England at Lord's four-and-a-half years ago.
New Zealand began the day on 334/1 but lost an early wicket before adding 241 runs for the loss of seven wickets across 65 overs. Kane Williamson made 31, sharing a 69-run third-wicket partnership with Conway, before becoming Justin Greaves' first wicket of the day.
Daryl Mitchell scored 11, Glenn Phillips 29, and Tom Blundell, returning from injury at No. 6, made four. Jacob Duffy was dismissed for 17, edging behind to wicketkeeper Imlach off Jayden Seales.
Late resistance came from Rachin Ravindra (72 not out) and Ajaz Patel (30 not out), who added an unbeaten 39 for the ninth wicket.
West Indies' bowling was disrupted by the absence of injured Kemar Roach, who will play no further part in the match. Seales, Anderson Phillip and Greaves each claimed two wickets, while Roston Chase bowled a marathon 44 overs.
In reply, the West Indies made a confident start, reaching 110 without loss from 23 overs at stumps. Brandon King advanced to 55 not out, while John Campbell, batting with an injured right hand, supported him with 45.
Despite New Zealand opening the bowling late with seamers Zak Foulkes and Michael Rae, runs flowed freely, and Ajaz Patel, playing his first home Test in almost six years, went wicketless.
Trailing by 465 runs, the West Indies threaten to turn the match into a high-scoring contest, leaving New Zealand in need of a sharper approach on Day 3. A home victory would seal a 2-0 series win and deliver valuable World Test Championship points.
Jacob Duffy took five wickets in the second innings to help New Zealand beat West Indies by nine wickets in the second Test in Wellington as the hosts went 1-0 up in the three-match series.
Justin Greaves says he will saviour a 'special day' after scoring a maiden double-century to help West Indies to an epic draw in the first Test against New Zealand in Christchurch.
New Zealand chased down a target of 162 to beat West Indies by four wickets to seal s clean sweep in the three-match ODI series at home.
New Zealand legend Kane Williamson has announced his retirement from T20 International cricket with immediate effect to focus on the other two formats of the game.
