New Order: Touched By The Hand Of God (1987)

From Discogs:

New Order's fifteenth single, released on Factory in December 1987 as 7", 12" and CD-Single.
Originally written for the movie soundtrack Salvation!, the single versions are much more refined and the title track was remixed by Arthur Baker.

The music video was directed by Kathryn Bigelow, and contains footage of the band hilariously dressed up as a hairy heavy-metal act. Also featured are actors Bill Paxton and Rae Dawn Chong.

I have the Canadian release, with Touched by the Hand of Dub on side b. The video is for the single version, not the extended version.