That was also Germany's last victory over Argentina in 16 games overall and avenged their 3-2 defeat to Diego Maradona's Argentines in the previous World Cup final in Mexico in 1986.
The Argentine bench also has a survivor from the 1990 final, then defender Nestor Lorenzo who is now one of coach Jose Pekerman's assistants.
Argentina had two men sent off in the 1990 game, the first red cards in a final. The match was settled by a late penalty from Germany's Andreas Brehme.
Argentina have since won twice and drawn once in friendlies and also finished 2-2 in the most recent meeting, a Confederations Cup match in Nuremberg a year ago.
"It is a much anticipated match because they are two big teams in world football, both have been world champions, we hope to play a great match," Pekerman said ahead of Friday's quarter-final in Berlin.
Klinsmann, who is looking to end Germany's "black series" of not beating one of the big football nations since 2000, said: "I'm very optimistic this is going to work out. It looks like the time to end this series and get into the semi-finals."
This will be the two rivals' fifth World Cup meeting. The Germans hold the edge with two wins and one defeat.
Argentina have won seven and lost five of their 16 matches going back to the first meeting at the 1958 World Cup. West Germany, then the holders, beat Argentina 3-1 in Malmo in a group game.
The sides met again in the first round in England in 1966 in a bruising 0-0 draw. Argentina went out to England in a 1-0 quarter-final defeat while West Germany progressed to the final where they lost 4-2 after extra time to the hosts.
The Germans won the 1954 and 1974 tournaments as West Germany and also lost the 1982 and 2002 finals. Argentina lost the 1930 final and won the first of their two titles in 1978.
Played 16: Germany won 5 drew 4 lost 7 - goals 22-23
2005 Confederations Cup Germany 2 Argentina 2 Nuremberg
2005 friendly Germany 2 Argentina 2 Duesseldorf
2002 friendly Germany 0 Argentina 1 Stuttgart
1993 friendly Argentina 2 Germany 1 Miami
1990 World Cup final Germany 1 Argentina 0 Rome
1988 Four Nations Cup Germany 1 Argentina 0 Berlin
1987 friendly Argentina 1 Germany 0 Buenos Aires
1986 World Cup final Argentina 3 Germany 2 Mexico City
1984 friendly Germany 1 Argentina 3 Duesseldorf
1982 friendly Argentina 1 Germany 1 Buenos Aires
1981 Mini World Cup Argentina 2 Germany 1 Montevideo
1979 friendly Germany 2 Argentina 1 Berlin
1977 friendly Argentina 1 Germany 3 Buenos Aires
1973 friendly Germany 2 Argentina 3 Munich
1966 World Cup group Germany 0 Argentina 0 Birmingham
1958 World Cup group Germany 3 Argentina 1 Malmo