While the rest of the players tried to cool down the situation, the referee felt the line had already been crossed and sent off both Dzeko and Papadopoulos.
Dzeko and Kyriakos Papadopoulos saw red in the 79th minute, the former receiving a second yellow after pulling down the shorts of Sokratis Papastathopoulos.
The Greek Football Federation (EPO) has condemned the display of banners referencing the Srebrenica massacre during Greece's World Cup qualifier against Bosnia-Herzegovina.
Greece's Sokratis Papastathopoulos and Bosnia and Herzegovina's Edin Dzeko clash.
Edin Dzeko has successfully taken football to a unusual new place after he pulled an opposition player's shorts down during a game.
Dzeko was not the only man punished, though, as his Greek counterpart was handed a straight red card by referee by Jonas Eriksson for his part in the altercation.
The draw left Bosnia third in Group H, three points behind Michael Skibbe's Greece, who sit in second behind leaders Belgium.
His side were leading 1-0 when he was sent off but the game ended in a draw, after Giorgos Tzavelas crashed home a 25-yard equaliser in the fifth minute of added time.
"They said I started the fight myself, but how could I do that if I was the only one to have fallen to the ground?"
"I feel like we lost 3-0".
Greece went on to salvage a point. "They didn't even deserve a 1-0 loss, they deserved to lose 4-0".