Skipper Tamim Iqbal hit 50 to help the side chase the target in 33.2 overs after the West Indies was bowled out for 148 in 43.4 overs.
All-rounder Shakib was back after being given a two-year ban by the International Cricket Council in October 2019, with one year suspended, for failing to report approaches from a bookmaker.
No primary contact to the leg-spinner has been established as the West Indies touring squad has remained in individual isolation since their arrival.
West Indies are the reigning champions in the T20 World Cup and the only team to have won the tournament more than once.
The Cricket West Indies (CWI) selection panel on Tuesday named the West Indies Test and ODI squads for the upcoming tour of Bangladesh.
Kyle Jamieson took five wickets to leave West Indies struggling at 124/8 on day 2, after New Zealand put a total of 460 in the first innings.
Put into bat, the Black Caps reached 294/6 at Stumps with Nicholls and Kyle Jamieson remaining unbeaten.
Both are set to return to the Caribbean: Roach due to the death of his father, and Dowrich for personal reasons.
A 2-0 series win over the West Indies likely will be enough to lift New Zealand above England into third place on WTC standings.
Cricket West Indies have been awarded for their courage of sending the men's and the women's team to tour England amid the COVID-19 pandemic that had caused a massive disruption to cricket's calendar year.
New Zealand declared their innings on 519-7, while West Indies had added 49 runs without a wicket at the end of day 2.
Kane Williamson scored 251 in the first innings of the Test against West Indies, which is also his highest Test score.
New Zealand was 243-2 at the end of a rain-shortened day with Williamson on 97 not out — on the verge of his 21st test century — and Ross Taylor on 31.
Black Caps are fourth in terms of percentage points won, the factor that determines the final placings, following a change to the points system announced last week
The teams left the field due to rain after just 2.2 overs on Monday night, with the West Indies at 25/1, and were never able to return, with the game being called off at 9.20pm local time.
After putting a mammoth score of 238/3, the Black Caps restricted the visitors to 166/9 in their allotted 20 overs to take an unassailable 2-0 lead in the three-match series.
In a rail-curtailed 16-over match, the Black Caps chased down the 176-run target with four balls to spare to take a 1-0 lead in the three-match series.
Most of the members of the West Indies squad had arrived from the UAE after competing in the Indian Premier League on November 14.
CWI assured that the "best available" team will be sent for the tour in January comprising three Tests, as many ODIs and two T20Is but wants the five-day games to be reduced.
Talking about the decision to drop Hope, Cricket West Indies' chief selector Roger Harper said that he was not "at his best" in the longest format of the game for a while.
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