Those two games are the most important in what has developed into one of the game's great rivalries and the latest instalment and 19th in all takes place on Saturday when they meet in Cape Town battling for a place in the World Cup last four.
Current Argentina coach Maradona was at his peak in 1986, as he captained his country to their second World Cup, scoring five goals on a run culminating in a thrilling 3-2 final victory over the then-West Germany.
Some of the game's most iconic images were carved in the Mexico sunshine - Maradona poised, ball at feet, about to take on a line of six Belgian defenders, Maradona punching the ball past Peter Shilton for his infamous "hand of God goal" and Maradona, slaloming through the English defence to score one of the all-time great World Cup goals to settle the quarter-final.
In 1990, Argentina kicked and fought their way to the final but by the time they faced the Germans again they were hampered by suspensions to key players and Germany ground out a revenge 1-0 win via a late Andreas Brehme penalty with a near burnt-out Maradona's team having two men sent off.
For current Germany manager Low, struggling to make an impact as a player in the 80s and embarking on his coaching career by the 1990 tournament, Maradona was everything.
"These games have a long history but during that time Maradona had a phase which was so strong and dominant that he defined an era like no other player," Low said on Friday.
"MAGICAL"
"He was magical with his game. With his creativity and invention he galvanised the whole world. In 1986 he was at his peak where he almost single-handedly decided the Cup in Argentina's favour."
Low had a much closer view of the teams' next World Cup meeting, as Germany triumphed on penalties in the quarter-finals after a 1-1 draw in Berlin four years ago.
As assistant to Jurgen Klinsmann he had seen the teams battle out two 2-2 draws the previous year - one in the Confederations Cup and one friendly -- and though there was nothing friendly about the 2006 clash, which ended with a mass brawl after the shoot-out, Loew said the aftermath was not a fair reflection of the match.
"There was a bit of an escalation but that should not be in in our heads. I never thought it was unfair or violent - it was hard-fought for 120 minutes," he said.
"They are passionate and are fully committed. They are at the limit, as are all South American teams, but they do what is allowed.
"They are also very strong physically, you saw that in 2006 but also in March when we lost the friendly 1-0 in Munich."
That win, decided by a Gonzalo Higuain goal, was Argentina's eighth in the series that began in the 1958 World Cup with the first of West Germany's four wins (including the 2006 shootout)
Which way the 19th goes on Saturday remains anyone's guess.
"Both teams are capable of beating each other, we know it will be another cut-throat game," said Low, who fittingly gave his last words on Maradona.
"He was always an attacking player," he said. "And that is where he will want to leave his mark as a coach."
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