We present both theoretical and experimental demonstrations of geometric phase transitions in a synthetic two-level photonic system. We demonstrate the use of this nontrivial phenomenon to achieve an unprecedented birefringence change detection, with a precision up to $\Delta n \sim 10^{-11}$. This result represents a significant improvement of three orders of magnitude over conventional techniques (typically limited to the level of $\Delta n \sim 10^{-8}$). In this system, two orthogonal polarizations of light constitute the effective two-level system, which is driven by a birefringence-sensitive synthetic magnetic field. A given photonic spin is able to precess around the 'magnetic' field and exhibits topological transition in its evolution trajectory in parameter space. We establish a direct relationship between the geometric phase transition and birefringence change, which is the basis of our detection technique. This approach significantly improves detection sensitivity and stability as compared to previous detection techniques. Moreover, the presented results benefit many fundamental and applied research fields such as structured light shapings and photonic switchings.