The Greeks restricted their hosts to just two shots on targets, despite the Spaniards having 80% possession.
It was especially important for the Greek team as they celebrated the 200th anniversary of the 1821 Revolution.
"It is a very good result for us. We are happy. We got a point against one of the best teams in the world. However, we have another game. We have not won anything, it is a great result, but we have a long way to go," Greek midfielder Carlos Zeca said after the match.
"We came to win. We know it's hard to win here, but we believed it. They created problems in the game, especially in the first half. There we thought that 0-0 is good. We worked for that."
Greece are now second in Group B (Spain, Sweden, Greece, Georgia, Kosovo).
Spain v Greece lineup
- Spain:Simon, Marcos Llorente, Sergio Ramos, Garcia, Gaya, Canales, Rodri, Koke, Torres, Morata, Olmo. Subs: Sanchez, Porro, Diego Llorente, Gil Salvatierra, Fabian, de Gea, Thiago, Busquets, Martinez, Oyarzabal, Jordi Alba, Gonzalez.
- Greece:Vlachodimos, Bakakis, Papadopoulos, Tzavelas, Tsimikas, Mandalos, Zeca, Bouchalakis, Limnios, Bakasetas, Masouras. Subs: Svarnas, Kyriakopoulos, Mavropanos, Kapino, Dioudis, Fortounis, Giakoumakis, Mavrias, Siopis, Androutsos, Pavlidis, Tzolis.