The hosts, after being sent in, were powered by the two Jamaicans, Gayle and Samuels, in front of 11,000 countrymen.
Opener Gayle continued his prolific form since returning to the West Indies team a month ago, smashing nine sixes and eight fours in his 20th one-day century.
Samuels was less brutal, but no less effective in cracking seven fours and a six in his third one-day ton.
The pair shared a fourth-wicket stand of 129 off 116 balls that anchored the innings.
New Zealand, trying to rebound after losing the first match last Thursday, got a good start as Southee removed Lendl Simmons to an edge through to wicketkeeper Watling at 10-1.
But Gayle soon started to unleash his trademark power-hitting, pacer Kyle Mills the first to feel his force as he disappeared for three sixes in the fifth over.
No bowler was spared and the strapping Gayle reached 50 off 42 balls in the 14th over.
Dwayne Smith, who contributed 24 in a stand of 88 with Gayle, departed at 98-2 when he holed out to long-off off legspinner Tarun Nethula.
But Gayle found another sound ally in Samuels, the pair playing some majestic strokes during their century stand.
Gayle survived a loud caught behind appeal off Daniel Flynn's part-time left-arm spin at 98 and soon passed three figures for the 20th time, off 88 deliveries.
The milestone, coming in his 231st match, made Gayle the most prolific West Indies century-maker in ODIs, passing Brian Lara's 19 centuries.
Samuels completed his 50 soon afterwards, off 58 deliveries.
Gayle, trying for his 10th six, was eventually caught on the deep midwicket boundary off Mills at 227-3 in the 38th over.
When Southee prised out Kieron Pollard (8) and Dwayne Bravo (3) cheaply with yorkers, the hosts dipped to 272-5.
But Samuels and his skipper Sammy added 43 off 36 balls to ensure the total went past 300.
Samuels reached his third ODI century off the first ball of the final over, celebrating with a giant leap.
New Zealand's chase was always going to be tough and Rampaul removed opener Rob Nicol to a catch at midwicket at 24-1.
Narine further stunned the visitors when he removed Daniel Flynn (21) to a slip catch at 62-2 in the 12th over.
Guptill and Williamson battled back in a third wicket stand of 59 before Samuels made his mark with two wickets in successive overs.
Guptill, who hit five boundaries, lofted an easy return catch while left-hander Tom Latham fell cheaply as he chipped to midwicket at 125-4.
Williamson and Watling maintained New Zealand's flickering hopes in a stand of 70 for the fifth wicket.
But once Williamson was leg before to Rampaul, the result was hardly in doubt.
Watling smashed four fours and two sixes but the lower order could not help keep up with the lofty run-rate required.
The series continues in St. Kitts with the third one-day international on Wednesday.
