We present a new approach to example-based style transfer combining neural methods with patch-based synthesis to achieve compelling stylization quality even for high-resolution imagery. We take advantage of neural techniques to provide adequate stylization at the global level and use their output as a prior for subsequent patch-based synthesis at the detail level. Thanks to this combination, our method keeps the high frequencies of the original artistic media better, thereby dramatically increases the fidelity of the resulting stylized imagery. We show how to stylize extremely large images (e.g., 340 Mpix) without the need to run the synthesis at the pixel level, yet retaining the original high-frequency details. We demonstrate the power and generality of this approach on a novel stylization algorithm that delivers comparable visual quality to state-of-art neural style transfer while completely eschewing any purpose-trained stylization blocks and only using the response of a feature extractor as guidance for patch-based synthesis.