stereogum: That Song From Last Night's Six Feet Under

(from stereogum.com)
It's called "Breathe Me" by Sia. Interesting choice for the series finale. RightClickSaveAs and pretend you're Claire driving down the highway:
Sia - "Breathe Me" (MP3)

Bonus:
Sia - "Breathe Me (Mylo Remix)" (MP3)

Four Tet, Ulrich Schnauss, and Mr. Dan also have remixes worth searching out.