In Julius Caesar, what makes Antony's oration speech so powerful that the mob turns against Brutus?
Antony's speech is so powerful as he employs a variety of tactics to get the crowd on his side and against the conspirators. He proves himself to be a master manipulator, demolishing Brutus's arguments against Caesar without openly appearing to do so.
Antony makes a direct appeal to the people, drawing them in by claiming to be a plain-speaking man.
I am no orator, as Brutus is,
But, as you know me all, a plain blunt man,
That love my friend (III.ii.218-220)
He is also careful to avoid condemning Brutus and the other conspirators openly, referring to them with increasing sarcasm as 'honourable men' (III.ii.84) but skillfully undermines their claims that Caesar was dangerously ambitious, by recalling all the instances that Caesar showed himself to be a modest man of the people: crying with them, refusing the offer of a crown, and so on. This begins to change the collective opinion of the crowd:
If thou consider rightly of the matter,
Caesar hath had great wrong. (III.ii.110-111)
Antony also makes a great display of emotion, weeping openly and playing up the pitiful spectacle of the wounds on Caesar's body. This is quite enough to drive the crowd into a rage, but he works them up still further by reading Caesar's will which shows more evidence of the murdered man's generosity towards the people. By the end, the crowd are thirsting for revenge against the conspirators.
Antony's grief at Caesar's death is real, but the main purpose of his funeral oration is to manipulate the crowd, as is all too clear in his aside at the end:
Now, let it work. Mischief, thou art afoot;
Take thou what course thou wilt.(IIII.ii.261-262)