Midfielder Ninis struck on the hour with a low shot from outside the area and the visitors then put all their men behind the ball for the last 30 minutes to keep the home team out.
"At half-time I told our players we had to maintain a strong defence but also do a little bit more in attack," Greece's Portuguese coach Fernando Santos told reporters.
"We did a very good job in the second half and our team had chances to score."
A dull encounter played in hot and humid conditions in mid-afternoon was more notable for the defensive efforts of both sides, with no more than a handful of shots on target at either end.
Greece top the group with 17 points from seven matches. Croatia, who visit Malta later, are second with 13 points from six games and Israel have 13 from eight.
Israel still retain outside hopes of qualifying for a major tournament for the first time since the 1970 World Cup finals in Mexico.
Coach Luis Fernandez said Greece's extra experience was the difference between the two teams.
"We had to take risks and playing in the heat took its toll," explained Israel's French boss.
"We had many youngsters, a new generation. I will always be proud of these players and I will always support them."
