Gradients in fluid viscosity characterize microbiomes ranging from mucus layers on marine organisms and human viscera to biofilms. While such environments are widely recognized for their protective effects against pathogens and their ability to influence cell motility, the physical mechanisms controlling cell transport in viscosity gradients remain elusive, primarily due to a lack of quantitative observations. Through microfluidic experiments with a model biflagellated microalga (Chlamydomonas reinhardtii), we show that cells accumulate in high viscosity regions of weak gradients as expected, stemming from their locally reduced swimming speed. However, this expectation is subverted in strong viscosity gradients, where a novel viscophobic turning motility - consistent with a flagellar thrust imbalance - reorients the swimmers down the gradient and causes striking accumulation in low viscosity zones. Corroborated by Langevin simulations and a three-point force model of cell propulsion, our results illustrate how the competition between viscophobic turning and viscous slowdown ultimately dictates the fate of population scale microbial transport in viscosity gradients.