Make something great out of a bad situation
[She] knew how to make a gourmet meal out of leftovers.
An example, admittedly of the literal usage, can be found in 'Beyond Passing' By Elaine Galindo
The parallel form would be
She made a gourmet meal out of [mere] leftovers.
Perhaps "snatched victory from the jaws of defeat" suggests what you'd like -- a last-minute success in an unlikely situation.