Satellite observations are used to establish the dominant magnitudes, scales, and mechanisms of intraseasonal variability in ocean dynamic sea level (ζ) in the Persian Gulf over 2002-2015. Empirical orthogonal function (EOF) analysis applied to altimetry data reveals a basin-wide, single-signed intraseasonal fluctuation that contributes importantly to ζ variance in the Persian Gulf at monthly to decadal timescales. An EOF analysis of Gravity Recovery and Climate Experiment (GRACE) observations over the same period returns a similar large-scale mode of intraseasonal variability, suggesting that the basin-wide intraseasonal ζ variation has a predominantly barotropic nature. A linear barotropic theory is developed to interpret the data. The theory represents Persian-Gulf-average ζ () in terms of local freshwater flux, barometric pressure, and wind stress forcing, as well as ζ at the boundary in the Gulf of Oman. The theory is tested using a multiple linear regression with these freshwater flux, barometric pressure, wind stress, and boundary ζ quantities as input, and as output. The regression explains 70%+/-9% (95% confidence interval) of the intraseasonal variance. Numerical values of regression coefficients computed empirically from the data are consistent with theoretical expectations from first principles. Results point to a substantial non-isostatic response to surface loading. The Gulf of Oman ζ boundary condition shows lagged correlation with ζ upstream along the Indian Subcontinent, Maritime Continent, and equatorial Indian Ocean, suggesting a large-scale Indian-Ocean influence on intraseasonal variation mediated by coastal and equatorial waves, and hinting at potential predictability. This study highlights the value of GRACE for understanding sea level in an understudied marginal sea.