pull one out of the hat

To find sudden and/or unexpected success in a situation that seemed otherwise hopeless or likely to fail. An allusion to the classic magic trick of pulling a rabbit (or other object) 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 don't know how you did it in so little time, but you pulled one out of the hat throwing this party!

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.