Worker was particularly impressive and managed to hog a large share of the strike.
Munro clattered the bowlers and got to 49 off 36 balls; fellow leftie Worker departed for 57 in the next over but New Zealand were well placed to press on.
Captain Kane Williamson and Ross Taylor put on 57 for the third wicket before Williamson, who seemed well set, played a defensive shot at Jason Holder and played the ball down onto his stumps, on 38.
By that stage the target was 74 in plenty of overs and when Tom Latham went lbw to the tidy Ashley Nurse, New Zealand were still 48 runs away.
Henry Nicholls edged Holder to the wicketkeeper but Taylor and debutant Todd Astle got New Zealand over the line with four overs to spare.
Taylor was left stranded on 49 off 76 balls as Rovman Powell bowled a wide to confirm New Zealand's win.
Earlier, the West Indies had Powell to thank for getting up to a reasonable competitive score.
The tourists were in trouble at 134 for five at 30 overs, but opener Evin Lewis, with a classy 76, and Powell, who was out on the penultimate ball for 59 ensured the West Indies would put up some sort of target.
The innings began cautiously, just a solitary wide off the first four overs.
Chris Gayle took a six and four off consecutive Tim Southee balls before edging Doug Bracewell's first ball in international cricket for 15 months to the wicketkeeper.
Shai Hope got the faintest of inside edges to Bracewell, was given out, immediately went to the DRS which confirmed a tiny spike on the screen. Hope was unhappy, Bracewell jubilant.
Lefthand opener Evin Lewis, after a quiet start, found his range and played a quality innings. He was full of back foot drives and lofted shots over the infield in completing another ODI half century to go with two hundreds.
His best support came from fellow lefthander Shimron Hetmyer, who was only called into the squad a few days ago when veteran Marlon Samuels was ruled out by a hand injury.
The pair put on 62 before Hetmyer lofted legspinner Astle to long off for the first of his three wickets.
Jason Mohammed was beaten for pace by Lockie Ferguson, and Holder fell to a spectacular one-handed catch above his head by Ross Taylor at slip.
Lewis pulled Bracewell for six but was given lbw off Astle on 76, off 100 balls, and because Hope had earlier called for the DRS, the West Indies had no referrals left.
From there the West Indies limped along – Trent Boult conceding a solitary single in the 39th and 41st overs – and would have been lost without Powell.
He clouted Ferguson into the car park at square leg and worked the ball around impressively. When he took 6, 6, 4 in the first three balls of the 49th over from Boult he had his first ODI half century, off 47 balls. The West Indies would have been lost without him.
Boult's final over cost 20 as Powell put some late punch into the West Indies innings.
He thumped Bracewell for another straight six in the 50th before being caught on the long off boundary, his 59 off just 47 balls.
Astle made the best of his debut opportunity, finishing with three for 33 off his 10 overs. His wrong'un was working well and he kept to an impressive line and was well rewarded.
Bracewell also had handy figures to savour on his return to the national team, taking four for 55 off eight overs.
New Zealand have now won 25 and lost 30 of their 63 ODIs against the West Indies.
The second game in the three-match series is at Christchurch's Hagley Oval on Saturday.
