The Greeks, using a fast counter-attacking game and solid defence, shook off their image as a team prone to international failure with a stunning victory and are now eager to prove it was no fluke when they face Spain, who beat Russia.
"A draw would suit us but we cannot consider this," Greece striker Zisis Vryzas said. "We must play to win."
The Greeks will finish their Group A games against Russia on June 20 by which time they hope to be in pole position.
Free from injuries for the first time since they started their European Championship preparations in late May, Greece will rely heavily on their tight rearguard and fast breaks from the back to crack open the experienced Spanish defence.
The Spaniards are ready to take revenge after their 1-0 home defeat to Greece in the qualifying campaign.
"They beat us in the qualifiers so we cannot say we are the favourites," Spain defender Carles Puyol said.
Spain are expected to continue with the attacking style that earned them a 1-0 win over the Russians in their opening match.
Coach Inaki Saez has broken with his own tradition by refusing to reveal his starting lineup for fear of suffering the same fate as their Iberian neighbours.
However, he has hinted at changes including bringing in pacy striker Fernando Torres for Fernando Morientes to give the tall Greek central defenders Traianos Dellas and Michalis Kapsis a tougher time than they faced against a disappointing Portugal.
Xabi Alonso is an option in central midfield, as Saez also looks for a speedier delivery of the ball out to the wings.
Greece coach Otto Rehhagel could rest Giorgos Karagounis and bring in defensive midfielder Costas Katsouranis to protect the back line, while fit-again striker Demis Nikolaidis could be back in the starting lineup after coming on against Portugal.
Probable teams:
Greece: (5-3-2) 1-Antonis Nikopolidis; 2-Yourkas Seitaridis, 19-Michalis Kapsis, 5-Traianos Dellas, 21-Costas Katsouranis, 14-Takis Fyssas; 8-Stelios Giannakopoulos, 6-Angelos Basinas, 20-Giorgos Karagounis, 10-Vassilis Tsartas; 15-Zisis Vryzas, 9-Angelos Haristeas (or 11-Demis Nikolaidis).
Spain: (4-4-2) 23-Iker Casillas; 5-Carles Puyol, 3-Carlos Marchena, 6-Ivan Helguera, 15-Raul Bravo; 17-Joseba Etxeberria, 4-David Albelda, 16-Xabi Alonso, 14-Vicente; 10-Fernando Morientes (or 9-Fernando Torres), 7-Raul.
More from rediff