Portugal, also resting defender Pepe and midfielder Raul Meireles, had the better of the game at the Estadio Nacional and should have been ahead inside the first 10 minutes.
Eder headed Nani’s curling cross straight at Greece goalkeeper Orestis Karnezis from close range in the second minute and Ricardo Costa was also foiled by Karnezis after he escaped his marker at a corner.
Greece struggled to create chances and a long range strike from Vassilis Torosidis was the sum of their efforts in a poor first half.
Striker Kostas Mitroglou was an isolated figure up front, where he was reduced to chasing down long balls.
Greece introduced veteran captain Giorgos Karagounis at half-time with Portugal bringing on experienced striker Hugo Almeida but neither player made an impact.