The damage had been done on Saturday, as England collapsed to 122-9 in their second innings, leaving the Black Caps on the verge of their first Test series win in England since 1999.
Trent Boult sent Olly Stone back to the pavilion with the first delivery of day four, leaving New Zealand chasing a mere 38.
Devon Conway was dismissed in the second over, though stand-in captain Latham (23) ticked off a milestone as New Zealand cruised to a maiden Test win at Edgbaston, setting themselves up for the ICC Test Championship final against India in emphatic fashion.
Any possibilities of complacency creeping in from New Zealand were dashed before a minute of play, Boult’s supreme delivery nicking off Stone’s edge and through to Tom Blundell.
A maiden over from James Anderson – whose record-setting Test match has not gone according to script – kept Latham, six off his 4,000th run in the longest format, at bay, and Stuart Broad subsequently gave the crowd something to cheer.
Conway fished at a delivery outside his off stump, with James Bracey gathering it in.
Latham and Will Young knew the Test was won, though, with sensible shots from New Zealand’s stand-in skipper ticking him towards the landmark, which came when he nudged Broad for a single.
Mark Wood very nearly ran Latham out with an acrobatic, underarm throw from close range, though even that wicket would have been immaterial.
After clipping a brilliant shot through backward point, Young dragged a wider Stone delivery onto his stumps, but Latham fittingly had the final say.
A sublime flick to the legside boundary was followed up by a deft touch through to third man to seal a 1-0 series win, just New Zealand’s second in England.
No home comforts for sorry England
England’s footballers get their Euro 2020 campaign started on Sunday, and the Edgbaston crowd were singing “football’s coming home” as they watched the cricketers learn a brutal lesson in the Birmingham sunshine.
Joe Root’s team, who have lost a series on home soil for the first time since 2014, do not convene again until they host India in August. While they had injuries to key players, along with off-the-field issues that marred the first Test, England have much to improve on, with their batting once again letting their bowling attack down.
Black Caps top the rankings as dominance over England rolls on
With this triumph, New Zealand have moved ahead of India to the top of the ICC Test rankings, though the ultimate test will of course come in the inaugural ICC Test Championship final against Virat Kohli’s team in Southampton next week.
New Zealand may have ended a dismal run in England, but overall, they have now not lost a Test to them since 2015 – a run of seven.