Fernando Santos's team were in the ascendancy for long periods but claimed all three points only thanks to Martin Skrtel's own goal which followed a woeful error by Slovakian goal keeper Jan Mucha.
Mucha was left red-faced after he took his eye off the ball as Liverpool defender Skrtel rolled a simple back pass which eased under the goalkeeper's foot and across the line.
That proved to be enough for Greece as the win lifted them level on 22 points with group leaders Bosnia heading into the final matches on Tuesday.
The Greeks, who are guaranteed at least a place in the playoffs, face Liechtenstein at home and are likely to win. Bosnia, who have a far superior goal difference, travel to Lithuania knowing a win will send them to the finals for the first time but a draw would probably open the door for Greece.
- Sports & Recreation
- Martin Skrtel