For Iago, the moment of truth comes very late in the play, when Emilia reveals his duplicity involving the handkerchief that Othello gave Desdemona:
O thou dull Moor! That handkerchief thou speak'st of
I found by fortune and did give my husband;
For often with a solemn earnestness,
More than indeed belong'd to such a trifle,
He begg'd of me to steal it.
Othello realizes, to his horror, that he has been duped into murdering his innocent wife. At this point, Iago's trickery is revealed, and the seeming spell he has over Othello is broken. Othello charges at him with his sword, and Iago kills his wife. As Lodovico and Gratiano arrive to discover what has transpired, Iago swears he will not reveal anything about his plot, saying:
Demand me nothing; what you know: you know.
From this time forth I never will speak word.
Gratiano replies ominously that torture will cause him to speak. So it is at this point that Iago finally experiences his moment of truth, even if the audience is denied the pleasure, and the sense of justice, of hearing a full confession or witnessing Iago's death.