Conway, the South African-born batsman who qualifies for New Zealand next September, already had 261 to his name after a commanding display on the opening day in Wellington and reached his triple century from 334 balls with a punch down the ground.
It was just the eighth triple century scored in New Zealand, the sixth in the Plunket Shield and also the highest score at the Basin Reserve overtaking Michael Papps' 316 not out in 2017-18. Bert Sutcliffe's 385 for Otago against Canterbury in 1952-53 is the highest first-class score in New Zealand.
He finished sat between Papps and Dean Brownlie's 334 in 2014-15 and could have pushed further up the list had Michael Bracewell not called a halt shortly before lunch on the second day.
It is worth noting as well that Wellington were 20 for 3 and 54 for 4 on the opening day before Conway took his formidable hold on the innings. He dominated stands of 129 with Malcolm Nofal (129), 173 with Peter Younghusband (36) and 159 with Jamie Gibson (65).
It seems a matter of when, not if, Conway will play for the New Zealand when his qualification period is completed. He has spent time around training squads in the last few months and had his credentials talked up by New Zealand coach Gary Stead.