Maradona put on a show for the 60,000-plus Scottish crowd and scored the third goal – and his first for his country – in a comfortable 3-1 win for the then world champions.
The performance left McGarvey a life-long fan of the attacking midfield maestro and saddened to hear that the 60-year-old had died.
The Argentina World Cup winner and the national team's former manager had been in hospital in Buenos Aires after surgery to remove a blood clot on the brain earlier this month.
McGarvey told the PA News agency about one of his fondest football memories.
He said: "I was told to look out for this teenager, who was the real deal.
"He looked like a wee boy but he was unbelievable. He tore us to shreds.
"He had speed over five yards and then speed to get away from you.
"I remember chasing him. I was quick and he had the ball but he was running away from me and so I left him to David Narey and Paul Hegarty and went to mark someone else. He was too good for me. He was outstanding in every way.
"After that game I kept a close eye on what he was doing and what a player he became.
"He won the 1986 World Cup by himself and he done it in style.
"And in the England game he scored probably the greatest goal ever, beating half the England team and then go past the keeper to score.
"Messi and Ronaldo are great players but nowhere near Maradona, he is the greatest.
"It is a very sad day for me. He is the greatest player I will ever see."