There are two catches here, though. First, you'll only find these low prices by searching through Kayak (Priceline and Orbitz show significantly costlier flights). So much for Captain Kirk's vaunted negotiation skills.
Second, and more importantly, the travel times can get pretty long, depending on the day you fly and your home airport -- that $286 fare from Orlando, for example, comes with an insane 13-hour layover in Lima, Peru. But hey, since Peru doesn't require Americans to get a visa, you can use that time to explore Lima's killer food scene or down a few pisco sours. It's win-win! As much as a 13-hour layover can be.
Make sure you put in IGU as your destination airport from any of the cities listed above, and search August through November for the crazy deals. Just don't forget -- Brazilian visas for Americans run $160, so factor that into your plans if you book this crazy-cheap deal.