They put on a staggering 323 for the first wicket on day one of the third test against the West Indies at Bay Oval.
Latham nicked off late in the day for 137 — his second century during the series.
Conway is undefeated on 178 and Otago seamer Jacob Duffy (9 not out) has joined him at the wicket in the nightwatchman role.
The Black Caps will resume on 334 for one and they have completely bossed the game so far.
For decades, Edgar and Wright remained the gold standard opening partnership for New Zealand.
They teamed up for 1655 runs in 56 test innings for their country.
But like stone wash, Pac-Man and Stubbies, they have been relegated to nostalgic value.
Latham and Conway are the new kings. They have combined for 1721 runs in 43 innings at the top of the New Zealand order.
Edgar and Wright had reigned since 1986.
It was not the last trivial pursuit question which will need revisiting.
It was New Zealand’s first 100-run opening stand against the West Indies in 23 years and the first against the West Indies in New Zealand since 1969.
They became just the eighth pair to put on a partnership of 300 runs or more.
They were closing in on New Zealand’s all time partnership record against the West Indies of 387 set by openers Glenn Turner and Terry Jarvis in Georgetown in 1971-72 before Latham’s demise.
The day started out in sedate fashion.
Latham and Conway knuckled down during the morning session and completed the mission to get their side through to the break without loss.
It was a consummate performance. Solid. No thrills. Just two openers going about their job.
Conway emerged from the break in a different mood.
He brought up 50 with a glorious drive down the ground.
Kemar Roach got clobbered again. He dug it in short this time, looking for some payback but got swung through mid-wicket.
He went for a third boundary in the over. Conway, who has endured lean patch in recent years, sent it to the rope at long-on to raise the team 100.
The South African-born left-hander was looking more like the player who burst on to the scene with a double ton on debut in 2021.
The West Indies were bleeding runs and they needed some intervention.
A passing rain shower gave them a brief reprieve and some time to gather their thoughts.
But the pair ploughed on and got through to the tea break with their wickets intact.
Conway had moved through to 120 — his sixth test century — and Latham was poised on 87.
The New Zealand skipper brought up his 15th test century after the break.
Only Kane Williamson (33), Ross Taylor (19) and Martin Crowe (17) have scored more centuries for New Zealand.
Conway tired noticeably late in the day.
He got a cramp in his top hand and had been hit earlier in the day. But it was Latham who made the mistake.
The left-hander edged a delivery from Roach to Roston Chase at second slip to bring an end to his long vigil.
