However, in stoppage time Georgios Samaras was awarded a penalty and he fired home the kick to send Greece through to the knockout stages.
Here, Sports Mole analyses the game to see if the Greeks deserved their win.
On target: 5
On target: 4
Was the result fair?
Greece were the better team in Fortaleza and as a result deserved to progress to the knockout stages of the competition. Santos's side created the better chances and could have been further ahead as Georgios Karagounis and Lazaros Christodoulopoulos went close before they were pegged back by Bony's goal. The Ivory Coast failed to get anything going to really stretch the Greeks bar the one error from Sokratis Papastathopoulos which allowed them back in the game. Although Samaras's penalty may have been slightly fortunate, he still had to put the ball away and he did just that, proving to be clinical for his side when they needed to be.
Santos's side were once again solid at the back for the majority of the game and seemed to swallow up everything the Ivory Coast had to throw at them until Papastathopoulos made an rare mistake. Defensively they were excellent as a team and continued to fight for every ball until the last minute, which helped them push on late in the game to get their winner. Kostas Manolas and Papastathopoulos were again magnificent at the heart of the defence and should continue to provide an excellent defensive wall for them in the tournament.
Going forward they were a lot more impressive then their first two outings as Karagounis, Dimitris Salpingidis and Christodoulopoulos all could have scored in the second half. Greece looked quick on the break and clinical when they got in the final third, which should stand them in good stead in the second round against Costa Rica.
Ivory Coast's performance
Judging by their display you wouldn't have believed that their fate in the World Cup was resting on a result in this game. Sabri Lamouchi's side were second best throughout and struggled for rhythm in the final third. They looked frustrated by the determination of the Greece backline and tried to be too cute with passes in and around the box. When they did get their goal it was a good move, but then they immediately sat back and invited pressure onto themselves, which would prove to be costly.
Their experienced players let them down as Salomon Kalou and Yaya Toure had the chance to end the game with a break in stoppage time, but instead of running to the corner Toure went for goal and wasn't successful. A poor performance and they deserved their fate. Sabri Lamouchi has announced that he is stepping down from his role as manager following his side's exit from the World Cup, ending his two-year tenure.
Sports Mole's man of the match
Andreas Samaris: Although the 24-year-old didn't start he had a major impact on the game after replacing Panagiotis Kone in the 12th minute. He scored his side's opening goal showing predatory instincts to latch on to a loose ball and fired past Boubacar Barry. In the second half he showed the defensive side of his game as he hassled the Ivory Coast midfield time and again and made several good interceptions. Samaris also showed in the final third to support his side on their counter-attacks to finish a very accomplished performance.
Cheick Tiote will not look back at this game fondly as he made the critical error of the game. He picked up the ball 25 yards from his own goal and decided to play a limp pass to Sol Bamba, which allowed Samaris to seize the ball and fire it past Barry. That moment seemed to sum up the Ivory Coast's performance.
Carlos Vera had a good game for the majority as he seemed to get most of his decisions spot on. The penalty decision on reflection is incorrect as Samaras appears to have caught himself with not a lot of contact from Giovanni Sio, but in the referee's defence it did look a spot kick in real time.
Greece: Greece take on Costa Rica in the second round of the World Cup on Sunday at the Arena Pernambuco.
Ivory Coast: Les Elephants face Cameroon in a friendly game in September following their exit from the competition.