On the quest towards full control over wave propagation, the development of compact devices that allow asymmetric response is a challenge. In this Letter, we introduce a new paradigm for the engineering of asymmetry in planar structures, revealing and exploiting unilateral excitation of evanescent waves. We test the idea with the design and experimental characterization of a metasurface for angular-asymmetric absorption. The results show that the contrast ratio of absorption (the asymmetry level) can be arbitrarily engineered from zero to infinity for waves coming from two oppositely tilted angles. We demonstrate that the revealed asymmetry effects cannot be realized using conventional diffraction gratings, reflectarrays, and phase-gradient metasurfaces. This Letter opens up promising possibilities for wave manipulation via evanescent waves engineering with applications in one-side detection and sensing, angle-encoded steganography, flat nonlinear devices, and shaping the scattering patterns of various objects.