As a very concrete example of a deep theorem different from the ones you've already mentioned, I'd nominate the Atiyah-Singer Index theorem and its more general cousins for consideration in your talk.

One basic advantage is that a heuristic introduction to this theorem is easily possible in a few minutes: just discuss two possible definitions of the Brouwer degree of a smooth map $f:M \to M$ on a compact finite dimensional smooth manifold $M$. First, there's the analytic definition which counts the number of inverse images weighted by the sign of the Jacobian. Then, there's the topological definition involving the action of $f$ on the orientation class. The fact that these two definitions give you the same integer is somewhat of a miracle even in this "simple" setting to an audience unfamiliar with the area. This motivates the vast generalization provided by the AS index theorem!