The Xanadu soundtrack was split in two parts. Side A was written by John Farrar - principle songwriter for Olivia - and performed by ONJ, with several guests backing her. Side B was written by Jeff Lynne of Electric Light Orchestra and performed by ELO - but the closing song was this one, with a guest lead vocalist.
So really, it's an ELO song. And the single - ELO's biggest hit - was billed to both of them.
At any rate, the song is a delightful coda to an abysmal movie.
Of course, we also published an ELO-only version on Totally Covered. Go check it out.