Integrating robots into human-centric environments such as homes, necessitates advanced manipulation skills as robotic devices will need to engage with articulated objects like doors and drawers. Key challenges in robotic manipulation of articulated objects are the unpredictability and diversity of these objects' internal structures, which render models based on object kinematics priors, both explicit and implicit, inadequate. Their reliability is significantly diminished by pre-interaction ambiguities, imperfect structural parameters, encounters with unknown objects, and unforeseen disturbances. Here, we present a prior-free strategy, Tac-Man, focusing on maintaining stable robot-object contact during manipulation. Without relying on object priors, Tac-Man leverages tactile feedback to enable robots to proficiently handle a variety of articulated objects, including those with complex joints, even when influenced by unexpected disturbances. Demonstrated in both real-world experiments and extensive simulations, it consistently achieves near-perfect success in dynamic and varied settings, outperforming existing methods. Our results indicate that tactile sensing alone suffices for managing diverse articulated objects, offering greater robustness and generalization than prior-based approaches. This underscores the importance of detailed contact modeling in complex manipulation tasks, especially with articulated objects. Advancements in tactile-informed approaches significantly expand the scope of robotic applications in human-centric environments, particularly where accurate models are difficult to obtain. See additional material at https://tacman-aom.github.io.