Jimmy Fallon Unpacks Trump's 'Bag' with Hillary

Jimmy Fallon finally hosted Hillary Clinton on his late night show -- and they did exactly what you'd expect ... took shots at Donald Trump.

The bit went like this -- Jimmy unpacked a brown paper bag he claimed Trump left behind from his 'Tonight Show' appearance. It was full of gag items, including a framed homage to Vladimir Putin.

Check out the clip -- Hillary gets in a couple jabs ... first at Jimmy, then at Putin. The Putin could potentially complicate things at a future state dinner.