We conduct a theoretical and experimental analysis for a self-referencing phase-locked module based on the delay-unbalanced Mach-Zehnder interferometer (UMZI) and optical phase-locked loop (OPLL) in a saturated absorption spectrum (SAS) frequency stabilization system. The designed self-referencing phase-locked system achieves significant suppressions of laser phase, frequency noise and modulation noise while keeping a highly stable frequency stabilization in both short-term and long-term. For the short-term performance, we achieve a laser linewidth compression of 3.3 MHz to 2 kHz, the laser phase noise is suppressed from -12.508 dBc/Hz to -95.461 dBc/Hz, and the frequency stability is improved from 2.663x10^-12 to 2.992x10^-13. For the long-term performance, the laser wavelength stability is improved from 3.113x10^-8 to 6.23710^-10. The proposed self-referencing phase-locked system provides a high-performance solution with both short-term and long-term performance of laser for spin-exchange relaxation-free (SERF) atomic sensor.