Othello is a play where evil does seem triumphant in the end, even if Iago is going to be arrested, imprisoned, tortured, and possibly later executed for his crimes. However, Iago's intent was to destroy Othello and he succeeded, at least in terms of his life's happiness and his reputation.
Iago preys on Othello's weaknesses to get him to believe Desdemona has been unfaithful to him even though there is scant evidence supporting this claim. He takes advantage of the ugly parts of Othello's nature—his pride, his easy jealousy, his anger—to get him to murder his wife. This in turn will ruin Othello's reputation, since he is already living on the edge of society, being both a Moor and a black man in a white European milieu where he is reluctantly prized as an asset to the military.
After Othello kills his wife and then subsequently learns the truth, Othello kills himself, both to avoid the public shame of what has happened but also to punish himself for killing the person he loved most. Can this ending be seen as evil triumphing over good? I would say yes and this makes Othello unique compared to most of Shakespeare's other tragedies. Only King Lear might have a bleaker finale.
Tragedies usually have sad but ennobling endings. Think of how Romeo and Juliet's double-suicide wakes their parents up to the destruction the feud brings to Verona—even though the lovers are dead, their deaths bring peace. Macbeth falls to corruption and is killed, but peace returns to Scotland thereafter. Same with Richard III, whose eponymous play is both a history play and a tragedy. However, in Othello, little good comes of the finale. Othello was a noble man and he was manipulated into doing evil. Iago will be punished, but he got what he wanted in the end, so in a strange way, evil is triumphant, even if the most evil character in the play won't be able to relish his success fully.