Pull a rabbit out of a hat

Meaning: To do something unexpected that may have seemed impossible; to get magical results.

Significado: Realizar una proeza, lograr lo imposible.

Traducción literal: Sacar un conejo de un sombrero.

Real examples:

Example 1: “Given that books are still (unless Steve Jobs and Bill Gates have pulled a rabbit out of a hat since  I wrote this) a one-way process, I’m going to find it very hard to see if I ask you to put your hands up…” (From the book Not Quite a Teacher: Target Practice for Beginning Teachers, by Tom Bennett) 

Example 2:

Example 3: “And would have been miserably defeated, Max, if you hadn’t pulled a rabbit out of a hat.” (From the book The Lights in the Sky are Stars, by Fredric Brown)