Take a really cool puppet act, add in NBC-level production values, sprinkle on a genius combination of "Singin' in the Rain"/"It's Raining Men," and you get yourself one grade-A mash-up. The transition is done through visual gags, but the recorded mix sure helps tie it all together.
Eat your heart out, Glee. This is how you connect two very different songs into an outrageous segment of musical television. I sure hope Those Funny Little People move on to the semi-finals of America's Got Talent so we get to see more of their excellent use of recorded music. At the very least, can we get a televised special of the ensemble doing this? Or a children's TV show? It is, after all, an adorable, funny, and charming puppet act. I could see a half-hour series with big music numbers developing very easily.