There was a brace of wickets for another Indian Premier League returnee Corey Anderson, and debutant tourists Scott Kuggeleijn.
New Zealand had been sent in - a move Latham said he would have made if he'd had the chance - on a slow pitch.
There was a brisk start, as Luke Ronchi did his early clattering routine, getting to 35 smartly. The opening stand was worth 70 in 10 overs, but the two key innings of the match came from Latham and belligerent Colin Munro near the end.
Latham produced a well-paced performance, getting to 104, his third ODI century, then getting out, down the pitch and being stumped off spin bowler George Dockrell.
Not noted as a big hitter, lefthander Latham hit four of them, to go with nine boundaries in his 111-ball innings.
Latham and Neil Broom put on 75 in 13 overs for the second wicket; Latham and Ross Taylor 67 for the fourth.
Taylor got his second half century of the series, 57 off 64 balls before whipping a full toss from medium pacer Barry McCarthy behind square where he was caught.
That came in the over after Anderson chopped a ball onto his stumps, having battled with his timing. Two wickets in the space of three balls meant a slowing of the run rate, which had been rattling along.
However Munro and Mitchell Santner put some muscle into proceedings.
Going into the last five overs, New Zealand were at 268 for five. Munro was largely responsible for 76 coming from the last 30 balls.
He clouted a frenetic 15-ball 44, with four sixes, Santner chipped in with 20 not out off nine and New Zealand moved out of sight of the Irish as rain swept across the ground at the end of the innings.
New Zealand, for whom the win gave them a 4-0 ODI record against Ireland, will finish the tri-series with their second game against Bangladesh on Wednesday night.
Corry Anderson said the game allowed players such as himself, Adam Milne and Matt Henry to get back to 50 over fitness after their IPL campaigns.
"It felt slightly heavier than normal, it was nice to get time on the legs, and running around for New Zealand," Anderson told the Radio Sport Breakfast.
"It's always exciting getting guys back in the groove with a few new faces. It's refreshing sometimes, not having the grind of the IPL intensity. It gets to you a little bit by the end of the tournament. It's nice to come to Ireland, with similar conditions to home.
"Getting back in camp with the Kiwi boys has always been my priority - it's always been the most enjoyable thing I do."
