The Moewe broke out its battle ensign and ordered the Otaki to stop but Captain Smith ignored the warning which led to the Moewe, armed with five guns and two torpedo tubes, firing at the Otaki and the Otaki, which only had a single gun, firing back.
The Otaki tried to outrun the Moewe but was unsuccessful and both ships became engaged in a fierce gun battle before the Otaki, which took 29 hits, was sunk - six people on the Otaki died including Captain Smith, and five on the Moewe died.
The Moewe, which had sustained seven hits and was badly damaged, rescued the survivors from the Otaki, who spent the rest of the war in Germany.
After the war, the captain of the Moewe, Nikolaus zu Dohna-Schlodien, said Captain Smith's battle with the Moewe was "as gallant as naval history can relate".
It led to Captain Smith receiving a posthumous Victoria Cross for bravery on that fateful day.
Captain Smith's wife, New Zealander Edith Broomfield, established an Otaki Shield award at her husband's old school, Robert Gordon's College.
This led to the awarding of the Otaki Scholar, to a high achieving senior student, who has visited New Zealand every year since 1937, except the World War II years.
The Otaki Scholar, funded by the New Zealand Government, visits Otaki College and other schools and partakes in various functions.
And since 2013 Otaki College has sent one of its students, known as the Sander Scholar, to Scotland for two weeks every January where they've been hosted by the college before touring the Scottish Highlands.
Dame Patsy said the monument would "remember not only those who died on the SS Otaki, but all those who lost their lives on ships during the First World War".
She said those on the Otaki would have been well aware of the dangers when they set out on their journey from London to New York.
"We can only imagine what ensued once Moewe broke out its battle ensign - the fear, the adrenaline and chaos of the engagement, the deafening gunfire, the shouting men and their despair as the Otaki began to sink."
She said the memorial would be "a lasting tribute to courage, a celebration of scholarship, and a reminder of the links that bind us both to our past and to our friends across the seas".
Otaki College principal Andy Fraser said among the six killed on the Otaki, was William Martin, aged only 14.
"Two weeks before he was killed he had been sitting behind a desk in a classroom in Robert Gordon's College in Aberdeen.
"He was mentioned in despatches bravely helping to load the Otaki's gun when he was killed."
Mr Fraser said a similar commemoration service was taking place at Robert Gordon's College.
"The services on both sides of the world will be recorded and shared between our two colleges such is the bond that we now have with each other."
He acknowledged the many people who took part in the ceremony but had special mention for college students.
"For you, today's reflection on events in the past will provide insights that, if acted upon, will help you to build the best possible future for yourself and for your country."
He also noted that the Merchant Navy, which was New Zealand's fourth service alongside navy, army and air force was "unfortunately forgotten by many and remembered by few".
Mr Fraser hoped the achievements of the Merchant Navy, which he felt hadn't been historically acknowledged enough, would become more widely known especially with events like the commemoration ceremony, which the college hoped to hold on an annual basis.
