It was 40 years ago, in 1972, when Greece scored two goals against Malta in a qualifying stage that, at that time, was included i nthe Eurocup.

Since then, Greece has won all its qualifying international matches with just one goal. The best example of this is the Eurocup won by Greece in 2004, in which Greece scored 1 goal every match in the quarter-final, semi-final and final:

Quarter-final
against France (the holders) – won 1-0, header from a right-wing cross.

Semi-final
against Czech Republic (the best team in the tournament) – won 1-0, header from
a right-wing corner.

Final
against Portugal (the hosts) – won 1-0, header from a right-wing corner.

Source: www.zonalmarking.net/2010/03/29/greece-euro-2004-tactics/