Shakespeare had already demonstrated to the reader that the Roman people are easily swayed with the opening scene in Act I. After the assassination of Julius Caesar, Brutus speaks to the crowd and convinces them that Caesar was ambitious and would have been a terrible leader. Although he is not a skilled speaker, he is able to use logos to convince that crowd that what he and the conspirators did was the best for Rome. At this point, they call for Brutus to become king.
Mark Antony, on the other hand, plays on the emotions of the crowd and incorporates three dramatic acts within his speech. First, he pauses to cry while speaking. This creates sympathy in the angry mob. Once they have been softened, he hints that Caesar had a will, but he says that he won't read it because it would anger them too much. The crowd cries for him to read the will (he never actually SHOWS what's written; he merely waves a scroll). He tells them that Caesar had made the citizens his heirs and that each one of them was going to receive gold. The fickle crowd, that had only moments before been ready to make Brutus king, begins to turn on the conspirators. The third dramatic act of Antony's is to display Caesar's body, and the throng becomes murderous. Afterwards, Antony's aside, "Mischief, thou art afoot" shows that he had planned to incite a riot with his speech.
By the end of each speech, they are completely behind the speaker. Brutus has the crowd so enthralled with him that they threated Antony before Antony has a chance to say anything. However, by the end of Antony's speech, they are running through the streets of Rome with swords, knives, and torches.
Brutus made a huge mistake. He not only granted Antony's request to speak at the funeral, he also told the commoners to hang around and listen. Actually, he commanded them to stay for Antony's speech.
Flavious and Marullus recognized the commoners tendancy to be sheep early in the play when they pointed out how everyone was excited about Caesar coming home from defeating Pompey. Apparently they had forgotten that Caesar had just defeated Pompey, who they were cheering for as a leader not too long ago. These commoners will stand behind whoever seems to be in charge at the time.