For natural microswimmers, the interplay of swimming activity and external flow can promote robust directed motion, for example, propulsion against (upstream rheotaxis) or perpendicular to the direction of flow. These effects are generally attributed to their complex body shapes and flagellar beat patterns. Using catalytic Janus particles as a model experimental system, we report on a strong directional response that occurs for spherical active particles in a channel flow. The particles align their propulsion axes to be nearly perpendicular to both the direction of flow and the normal vector of a nearby bounding surface. We develop a deterministic theoretical model of spherical microswimmers near a planar wall that captures the experimental observations. We show how the directional response emerges from the interplay of shear flow and near-surface swimming activity. Finally, adding the effect of thermal noise, we obtain probability distributions for the swimmer orientation that semiquantitatively agree with the experimental distributions.