Croatia were undone by two chances from corners that were converted by Giorgos Samaras and Fanis Gekas in a game that came to life in the second half.
The win puts Greece on 21 points, Croatia remain on 19 and the Greeks will qualify for the finals in Poland and Ukraine if they avoid defeat in Georgia on Tuesday because they have a better head-to-head record against the Croats.
"We had two finals to play and we have won the first one," Greece coach Fernando Santos told a news conference. "It's now up to us against Georgia.
"We haven't achieved anything yet. We want to celebrate after the game in Georgia, who are a good team and will have nothing to lose when they play us."
FEW CHANCES
The first 45 minutes produced few chances as both sides appeared to be affected by a stoppage in play after two minutes when Greek and Croatian fans threw flares and smoke bombs at each other. Croatia supporters also ripped up and threw seats.
English referee Howard Webb held up the game for five minutes so the trouble could be quelled.
After that, Greece found it difficult to break down the Croatia defence. Their only chance of note came in the 42nd minute when central defender Avraam Papadopoulos broke forward but his header was saved easily by Stipe Pletikosa.
Greece looked more threatening in the second half and scored in the 71st minute when the ball fell to the unmarked Samaras on the edge of the area following a Giorgos Karagounis corner. The striker's swerving volley found the bottom corner of the net.
Greece's second goal also came from a corner seven minutes later when Gekas found some space in the box and planted Karagounis's cross in the net.
Croatia offered little in response and must win their final game at home to Latvia to have any chance of qualifying.
Croatia coach Slaven Bilic said: "We expected Greece to try to score from a counter attack or a dead ball. We dealt with them fairly well but made two mistakes that cost us. Corners should not be a problem for us. They were two cheap goals."
"It's difficult to create chances against Greece because they defend very well but we didn't make the most of the chances we had," he added.
"There's still another game but Greece are the favourites to qualify. It's not in our hands anymore. We'll try to beat Latvia and then hope for the best."
