Adsorption to a surface, reversible-binding, and trapping are all prevalent scenarios where particles exhibit "stickiness". Escape and first-passage times are known to be drastically affected, but detailed understanding of this phenomenon remains illusive. To tackle this problem, we develop an analytical approach to the escape of a diffusing particle from a domain of arbitrary shape, size, and surface reactivity. This is used to elucidate the effect of stickiness on the escape time from a slab domain: revealing how adsorption and desorption rates affect the mean and variance, thus providing a novel approach to infer these rates from measurements. Moreover, as any smooth boundary is locally flat, slab results are leveraged to devise a numerically efficient scheme for simulating the sticky escape problem in arbitrary domains. This letter thus offers a new starting point for analytical and numerical studies of stickiness and its role in escape, first-passage, and diffusion-controlled reactions.