West Indies leaned on Kieron Pollard's top-score of 56 to post 264 all out off 49.3 overs at Warner Park.
New Zealand's pursuit was anchored by captain Taylor's 110 off 115 balls on his return from injury but no other batsman passed 35 as the Kiwis were bowled out for 240 with three balls remaining.
The skipper's sixth one-day ton in his 111th match contained six fours and five sixes.
Narine's miserly spell earned him the man of the match honor and the fiery Best claimed Taylor among his four wickets in his first match of the series.
West Indies lead the five-match rubber 3-1 with the final match at the same venue on Monday.
Earlier, the hosts recovered from 20-3 thanks to Pollard's circumspect half century, which was spiced with five fours and a six.
He got good support from Marlon Samuels (46), wicketkeeper Devon Thomas (37) and fellow allrounders captain Darren Sammy (26) and Andre Russell (29).
Tim Southee, who removed the dangerous Chris Gayle in his early burst, claimed 3-53 while Jacob Oram took 3-42.
West Indies won the toss and chose to bat and was in early trouble once Doug Bracewell claimed Johnson Charles (1) to a lofted catch to mid-off at 17-1.
Southee soon made two crucial strikes in his first over to remove Gayle (16) and Dwayne Smith (0).
Gayle hit a four and a six before he played across the line of an inswinger and was leg before wicket while Smith fell for a duck, edging an outswinger to Taylor at first slip.
Samuels forged a fourth-wicket stand of 39 with Dwayne Bravo, who contributed a busy 18 before he fell trying to be too ambitious.
Bravo was Oram's first wicket, mid-on Trent Boult running back 10 meters to haul in a well-judged catch at 59-4 in the 18th over.
Samuels and Pollard continued the rebuilding process by adding 46 for the fifth wicket.
Samuels was in sight of a half century when he played back to Nathan McCullum and was lbw to leave the innings at the crossroads at 105-5.
But Pollard and Thomas, in the team in place of Denesh Ramdin who was getting married, laid the platform for a challenging total with a level-headed association that realized 85 runs off 83 deliveries. Thomas contributed a career-best 37 off 43 balls.
Pollard's 50 arrived off 63 balls, his slowest in ODIs, but he couldn't go much farther. He was deceived by Oram's slower ball and skied off the top edge to point.
Sammy and Russell made sure Pollard's good work was not wasted, compiling useful cameos in the final overs. Sammy hit two sixes and a four in 26 off 22 balls while Russell slammed two sixes and two fours in 29 off 16 balls.
Best made an early strike when the Kiwis replied, Martin Guptill rushed by a full-length delivery and plumb lbw at 8-1.
Rob Nicol provided some impetus to the chase and added 48 with Brendon McCullum as New Zealand took the initiative.
But the returning McCullum (10) was prised out by Andre Russell, miscuing a pull to Sammy at short midwicket at 50-2 in the eighth over.
Sammy further dented the chase when Nicol's enterprising innings was ended when he hoisted the skipper straight to deep square leg at 63-3. Nicol struck three fours and two sixes off 32 balls.
West Indies took control when Narine struck for the first time, Kane Williamson lbw playing across the line at 75-4 in the 14th over.
Taylor dominated a stand of 71 with left-hander Tom Latham, who fell to Samuels' offspin after struggling to compile 32 off 62 deliveries.
Best returned to claim Nathan McCullum and removed the middle stump of Oram (6) at 219-7 and Taylor was left with only the tail to help him.
He hoisted Russell for 21 off one over to revive the flagging hopes of his team and arrived at his hundred, off 108 balls, with 41 still needed off 26 balls.
Narine claimed Doug Bracewell for 5 and once Taylor miscued a low full toss to be caught off Best, the match was as good as over.
Southee was the last to fall, comically run out as he tried to scamper a bye.