This paper develops a control strategy for pursuit-evasion problems in environments with occlusions. We address the challenge of a mobile pursuer keeping a mobile evader within its field of view (FoV) despite line-of-sight obstructions. The signed distance function (SDF) of the FoV is used to formulate visibility as a control barrier function (CBF) constraint on the pursuer's control inputs. Similarly, obstacle avoidance is formulated as a CBF constraint based on the SDF of the obstacle set. While the visibility and safety CBFs are Lipschitz continuous, they are not differentiable everywhere, necessitating the use of generalized gradients. To achieve non-myopic pursuit, we generate reference control trajectories leading to evader visibility using a sampling-based kinodynamic planner. The pursuer then tracks this reference via convex optimization under the CBF constraints. We validate our approach in CARLA simulations and real-world robot experiments, demonstrating successful visibility maintenance using only onboard sensing, even under severe occlusions and dynamic evader movements.