I also believe that you're referring to Act 2, scenes 2 and 3--the scenes in which Iago plans to get Cassio drunk so that when Roderigo provokes Cassio, Cassio will retaliate (and thus will be fired by Othello from the lieutenancy).
In Act 2, scene 2, Iago convinces Roderigo (who is in love with Desdemona) that Cassio and Desdemona are having an affair. While this claim seems ridiculous to audiences, Roderigo, who is so desperate to win Desdemona's love, believes it because Iago is so convincing. Iago tells Roderigo that the only way for Cassio to be out of the picture is for him to be dismissed from the lieutenancy, so convinces Roderigo to provoke him and start a fight. Further, Iago convinces Roderigo that Cassio is "rash and very sudden in choler, and haply may strike at you," and decides that if Cassio is drunk, the plan will be more successful.
Then, in an a brief soliloquy in Act 2, scene 3, Iago tells audiences of this plan to get Cassio drunk:
If I can fasten but one cup upon him,
With that which he hath drunk tonight already,
He'll be as full of quarrel and offense
As my young mistress' dog.
Ultimately, Iago's plan does lead to Cassio's dismissal from the lieutenancy, which is, obviously, a victory for Iago.
While Iago certainly persuades Othello to think and do many things, I think that you might have meant, "In what scene and act does Iago convince Cassio to get drunk?" That is a much more significant scene to the play's plot, and it takes place in Act 2, Scene 3. By getting Cassio to drink, Iago is able to stir him to fight with Cyprus's governor which causes Othello to fire Cassio. This serves Iago's plot to take Cassio's position and sets into motion Iago's bigger plan to bring down Othello.
If your question really is about Othello and Iago, Iago does encourage Othello to enjoy his wedding night (the festivities were postponed because Othello was sent to Cyprus) and to make merry. This is on the same night that Iago plans to get Cassio drunk and to make him look bad.