On the topic of mixing up genres, one of my favourite examples is by The Pogues, in The Broad Majestic Shannon

The musical interlude starts at 1 min 20 but then it changes at 1 min 30 to a brief part of the tune Give Me Your Hand, aka Tabhair Dom Do Lámh composed in the early 1600's by the blind Irish harpist Rory Dall O'Cahan, and performed by The Chieftains on the second video.

The fun thing about the song by The Pogues is that the first words sung after that tune are "Take my hand". Very clever!