So, first off, you nee to have the dinosaurs go extinct in Africa, Asia, Europe, and North America as usual, but survive in South America. In the Cretaceous period, North and South America were not connected by the isthmus of Panama -- they would not connect until around 2.7 million years ago during the Great American Interchange.
Next, you need to make sure that dinosaurs don't make it to Asia during the last ice age. This is the point where humans made it to the Americas, some 20-40,000 years ago, when lowered sea levels created a land bridge between modern Alaska and Russia. This shouldn't be too hard, since all of modern Canada and parts of the norther United States were covered in glaciers. Just make sure that the dinosaurs do not adapt to the cold too much and keep them closer to modern Mexico until the glaciers recede and the land bridge disappears.
The reason I say "sort of" is that since the dinosaurs died off, humans and all other mammals evolved from small rat-like animals. There are species, alligators are a good example, that have not changed their appearance very much since the Cretaceous, so I think you could make some plausible arguments, you just need to think about how dinosaurs evolved enough to survive extinction while still maintaining the size and appearance you want, and also think about what ecological niches they would fill to survive alongside all of the new mammal species first in South America for about 20 million years and then alongside a new host of North American mammals for another 3 million years before finally meeting humans.