First, when you look at your listeners (one at a time) you are paying attention to them. People love to have attention paid to them, and are more likely to pay you back with their attention.
Second, when you watch their faces, especially at the ends of your statements, you can see their expressions, and react accordingly. Your monologue thereby becomes a dialogue, which gives you greater influence.
Third, when you look at your listeners, you display belief in yourself and your point of view. Belief is infectious. It makes you more persuasive.
Look at your listeners. See your listeners. And notice what you see.