Mr Mackay, whose own wartime exploits in the London Scottish 1st Battalion included escaping from an Italian POW camp dressed as an enemy soldier, spotted Miss Steiner at the dance but was too shy to approach her.
He sent a friend over to ask if she would dance with him, but Miss Steiner insisted she would only dance with him if he plucked up the courage himself.
He did, and what followed was a whirlwind romance that saw her and her mother whisked back to Mr Mackay's native Scotland.
The couple married on July 17, 1946, and have been "wholly dedicated" to each other ever since.
With a family of two children, seven grandchildren and five great-grand-children, they worked as hoteliers before retiring to live at a care home in Broughty Ferry, Dundee.
According to the couple's daughter, Sharon Mackay, Edith Steiner and her mother survied six weeks in Auschwitz in June 1944.
Having come from the Székesfehérvár region of Hungary, Eci and her mother were the only members of their family who survived the ghastly selection process at Auschwitz.
While Edith and her mother were set to one side to work - itself usually a slow and lingering death - the other members of the family were sent straight to the gas chamber.
While at Auschwitz, Eci managed to make "keep sakes" she has kept with her ever since, including a comb and a poem book.
As the war drew to a close, and the Soviets advanced rapidly from the east, the Nazis marched camp inmates towards Germany to help tackle the desperate shortage of workers in factories and mines.
John himself was captured at Tobruk in North Africa in the early part of the war. A soldier with the London Scottish, he escaped an Italian prisoner of war camp with his friend dressed as Italian solidiers.
The pair had to keep moving for 18 months however, to avoid wolves and evade capture.
John, orignally from Glasgow, was also one of the first soldiers to be recruited by the SAS, said Sharon.
After returning to Scotland Eci and John owned the Atholl Arms Hotel in Pitclochry, before retiring and moving to Dundee.
The devoted couple, aged 96 and 92, will mark their 71st Valentine's Day tomorrow with a party.
Their advice to young couples is to be romantic all year round - and not just on February 14.
Pamela Shaw, activity coordinator at Bupa Balcarres Care Home, where the pair now live, said: "John is a true gentleman.
"He is always checking in to make sure Eci is happy and the pair still refer to each other as 'sweetheart' on a daily basis.
"Their devotion to one another is clear to anyone who spends even a short time in their company.
"John came to join us a year after Eci moved in, so it's wonderful that they are both near one another again. Our main aim now is to ensure that they continue to enjoy a happy life together.
"We're having a little party for all our residents this Valentine's Day, so it's lovely to have such a real example of true love with us at the home."
