West Indies was well on its way to chasing down New Zealand's total of 190-9 off 50 overs when rain halted their charge at 93-1 off 18 overs at Sabina Park.
But victory was sealed soon after resumption as they coasted to a revised target of 136 off 33 overs with 8.4 overs to spare.
Opener Gayle slammed three fours and five sixes in an unbeaten 63 off 57 balls, his third successive half century following two in the Twenty20 internationals last weekend.
Smith top-scored with 65 not out, spiced with six fours and three sixes off 77 deliveries.
The pair's match-winning, second-wicket stand was worth 130 unbroken off just 128 balls.
Earlier, fast bowler Andre Russell took 4-45 from 10 overs to stun the Kiwis and earn the man of the match award. Spinner Sunil Narine helped maintain the stranglehold with 2-26 while pacer Ravi Rampaul took 2-42.
Wicketkeeper BJ Watling top-scored for the visitors with 60 off 98 balls while allrounder Jacob Oram scored 32.
Russell made an immediate impact with the new ball, finding the edge of Martin Guptill's bat for captain Darren Sammy to snap up a low second slip catch.
Rob Nicol (14) and left-hander Daniel Flynn (12) shared a stand of 27 for the second wicket before Russell removed both in successive overs to further derail the innings.
Flynn tried to force through the off side and dragged onto his stumps while Nicol swatted a high catch to deep midwicket to leave New Zealand floundering at 33-3 in the 10th over.
Narine added to the Kiwis' woes by removing Dean Brownlie, plumb leg before wicket.
Sammy claimed opposite number Kane Williamson (24) to a wicketkeeper's catch at 71-5.
Watling and Oram put together a sixth-wicket stand of 46 to revive the innings.
Oram was the more aggressive, slamming two fours and two sixes.
He eventually fell to Rampaul, his stumps scattered by a slower ball off the last ball of the batting powerplay at 117-6.
Andrew Ellis (14) was Narine's second wicket, bowled trying to force through the off side, after sharing a stand of 44 for the seventh wicket with Watling.
Watling anchored the innings, his second half century arriving off 86 balls.
He was the ninth man out, leg before to Rampaul.
New Zealand claimed an early breakthrough as they tried to defend a modest total.
Kyle Mills provided the spark as Lendl Simmons deflected a leg side catch to a diving Watling on 8.
But there were few highlights for the visitors following that as Gayle and Smith dominated with some thumping strokes.
Gayle, in his first international in his home country for three years, was first to stamp his mark, launching Tim Southee for his first six and sending two more sixes sailing out of the ground off Nicol and Tarun Nethula.
Smith was equally punishing, finding the boundary regularly as well.
The stand was well established when lightning and thunder and heavy rain caused a two-hour delay and threatened to waste the good work from the hosts.
But the skies eventually cleared and both batsmen notched half centuries as they steered their team home comfortably to the adjusted target.
Smith was dropped just before the end, but the result was never in doubt by then.
The second match in the five-match series is at the same venue on Saturday.