By preparing a sensor system around isolated exceptional points, one can obtain a great enhancement of the sensitivity benefiting from the non‐Hermiticity. However, this comes at the cost of reduction of the flexibility of the system, which is critical for practical applications. By generalizing the exceptional points to exceptional surfaces, it has been theoretically proposed recently that enhanced sensitivity and flexibility can be combined. Here, an exceptional surface is experimentally demonstrated in a non‐Hermitian photonic sensing system, which is composed of a whispering‐gallery‐mode microresonator and two nanofiber waveguides, resulting in a unidirectional coupling between two degenerate counter‐propagating modes with an external optical isolator. The system is simple, robust, and can be easily operated around an exceptional surface. On the one hand, sensitivity enhancement is observed by monitoring the resonant frequency splitting caused by small perturbations. This demonstration of exceptional‐surface‐enhanced sensitivity paves the way for practical non‐Hermitian sensing applications. On the other hand, the suppression of frequency splitting around the exceptional surface is also shown for the first time.