Anna Wintour & Miranda Priestly Face Off in Vogue Shoot, Watch Video

No one is safe from Miranda Priestly's shade ... not even Anna Wintour.

The Vogue boss graced the May cover in a joint shoot with Meryl Streep, who was fully in character as the iconic "The Devil Wears Prada" antagonist.

In the issue's cover video, the magazine moguls can't quite place how they know each other ... despite both being famed fashionistas.

They ride the elevator to the top as ABBA's "Dancing Queen" plays in the background -- a nod to Meryl's role in "Mamma Mia" -- while sizing each other up.

In the end, they compliment each other's shoes before going about their busy days.

The character of Miranda was famously inspired by Anna -- but she doesn't take that for granted, telling Vogue ... "It’s such an honor to be played by Meryl, however distant Miranda is from myself. Who wouldn’t think that that wasn’t the most extraordinary gift?"