Optical sensors have become indispensable in various fields, ranging from gravitational wave detection to biomedical imaging and structural health monitoring. Target information is commonly encoded in the phase changes of optical signals. Enhancing the sensitivity to phase changes is crucial for detecting weak signals and extracting valuable data. Recently, exceptional points (EPs), a spectral singularity in non-Hermitian systems, have been explored in various physical systems for sensitivity enhancement. However, it requires precisely controlling the sensor parameters, which restricts the applicability of EP enhancement to certain types of sensors. To overcome this limitation, we propose a novel configuration to implement EP-enhanced sensing. In this approach, a conventional sensor is connected to a microresonator operated at EPs via an optical waveguide. The EP microresonator amplifies optical phase changes from the sensor, converting them into distinct and quantifiable resonance splitting in the transmission spectra of the system. As a proof-of-concept, we demonstrate a six-fold enhancement in the detection limit of fiber-optic strain sensing using this EP-enhanced configuration. By separating the EP control from the sensor to eliminate the need to finely tune the sensor, our configuration enables EP enhancement for a wide range of conventional sensors. This work provides a promising universal platform to apply EP enhancement to diverse phase-dependent structures for ultrahigh-sensitivity sensing in various applications.