Exceptional point (EP) is referred to degeneracies in a non-Hermitian system where two or more eigenvalues and their corresponding eigenvectors coalesce. Recently there have been significantly increased interests in harnessing EPs to enhance responsivities and achieve ultrasensitive detections in optics, electronics and acoustics, although there are few similar studies focused on using surface acoustic wave (SAW) sensing technologies, probably due to its great technical challenges. Herein, we proposed a scheme for accessing EPs in an on-chip architecture consisted of coupled-SAW-resonators system, forming a passive parity-time (PT) symmetric system. We demonstrated that by tuning additional losses in one of resonators and regulating the system in the proximity of the EP, the sensor exhibited significantly enhanced responses. As an example, we present an EP-based SAW gas sensor, which showed a much-improved sensitivity compared to that of a conventional delay-line SAW sensor. The fundamental mechanisms behind this excellent sensing performance have been elucidated.