Both sides struggled to hit the target in the first half, with Odion Ighalo squandering two chances for Granada by sending his efforts wide of the mark.
Ruben Rochina also came close twice, but he too missed the target on both occasions.
Ighalo was the closest to breaking the deadlock in the opening 45 minutes, heading Nolito's cross against the post from six yards out.
Rochina finally worked the opposition keeper for the first time shortly after the restart when Jose Maria Movilla had nodded the ball to him. He let fly from outside the box, but Tono was equal to it.
Ighalo was guilty of missing another chance just before the half hour mark having been slipped in by Diego Mainz. He tried to find the top left corner with his effort, but it flew past the post.
Rochina continued to find space to shoot in the opposition half, forcing Tono into a good, low save in the 64th minute with his effort from outside the box.