Boronic acid catalysis (BAC) was applied to the 1,3-transposition of allylic alcohols and the related Meyer–Schuster rearrangement of propargylic alcohols using highly electron deficient polyfluoroarylboronic acids as catalysts under mild metal-free conditions. A wide range of synthetically useful products are formed in E : Z selectivities superior to that of metal-catalyzed methods. A mechanism is proposed involving partial or full ionization into an allylic (or propargylic) carbocation, and additional possibilities for multicatalytic tandem reactions are exemplified.