Since Sophocles' Antigone is a tragedy, the resolution of the conflict actually ends very tragically, meaning with a great deal of sorrow and strife. Also, while the play's title reflects the importance of Antigone's death, the true tragic hero of the play is Creon, as his decisions and perspectives are the primary cause of Antigone's death. Therefore, as the tragic hero, the play's resolution actually revolves around Creon.
One of Sophocles' points in writing Antigone is to show the dangers of tyranny. He does this by portraying Creon as acting tyrannically by refusing to embrace anyone else's perspective but his own. He believes that Polynices should be treated as a traitor of the state and not given proper burial, even though he is family. The issue is that Creon's decree that burying Polynices is a crime punishable by death disobeys the gods' own decrees, as Antigone points out. Creon's greater fault, though, is that when he is told he is wrong, first by Antigone, then by Haemon, then by the citizens in general, he refuses to listen. Instead, when Haemon begs him to listen to others' council, saying, "Don't be so stubborn that you say you and you alone are right," Creon responds by saying it is his job as king to rule over the people, as we see when he replies, "The city will tell me how I ought to rule it? ... Isn't the city thought to be her ruler's?" (716-17, 745, 747).
However, finally the soothsayer Tiresias, along with the city's elders, are able to convince Creon he is wrong. Tiresias prophecies that the city will be plagued and that Creon will be punished by the gods for putting his own laws above the gods' laws, leading to the resolution. Creon finally consents, asks for advice, and agrees to free Antigone from the tomb, saying, "My judgement has turned and seen better ways" (1120). However, sadly, it is far too late. A messenger returns to report that both Haemon and Antigone have committed suicide inside the tomb; later, Creon's wife takes her own life as well. Creon remains alive, but his tragedy is that he has lost everyone that is dear to him. However, he has also learned the folly of his pride and stubbornness, and this revelation is the moment of resolution.