In multisensor systems, time synchronization is particularly challenging for underwater integrated navigation systems (INSs) incorporating acoustic positioning, where time delays can significantly degrade accuracy when measurement and fusion epochs are misaligned. This article introduces a tightly coupled navigation framework that integrates a passive inverted ultrashort baseline (piUSBL) acoustic positioning system, a strapdown inertial navigation system (SINS), and a depth gauge under precise time synchronization. The framework fuses piUSBL azimuth and slant range with depth measurements, avoiding poor vertical-angle observability in planar arrays. By combining synchronized timing with acoustic signal processing, the proposed method transforms delay from an unobservable error into a measurable parameter, enabling explicit quantification of both acoustic propagation and system processing delays. Field experiments demonstrate that the proposed approach reduces position RMSE by 44.02% and maximum error (MAXERR) by 40.79% compared to the uncompensated baseline while achieving further RMSE reductions of 37.66% and 35.82% in horizontal directions relative to filter-based delay compensation. The results confirm that explicit delay measurement outperforms filter-based estimation though instantaneous performance remains sensitive to acoustic signal quality, emphasizing the need for robust signal processing alongside accurate time synchronization in latency-sensitive multisensor systems.