pull one out of the hat

To find sudden and unexpected success in a situation that seemed otherwise hopeless. An allusion to the classic magic trick of a magician pulling a rabbit out of a seemingly empty hat. Wow, I didn't think you'd have the programming ready in time for launch day, but you really pulled one out of the hat! I thought we were going to have a drab Christmas, considering how much my boyfriend and I have been working lately, but I came home on Christmas eve to find the whole house decorated and a lovely dinner on the table. I don't know how he did it, but he pulled one out of the hat this year!

pull one out of the hat

bring off an unexpected trick in an apparently desperate situation.

The image here is of a rabbit pulled out of a magician's hat.

1971 James McClure The Steam Pig I must say you've really pulled one out of the hat this time.