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The origin of the tight scaling relation between the mass of supermassive black holes (SMBHs; MBH) and their host-galaxy properties remains unclear. Active galactic nuclei (AGNs) probe phases of ongoing SMBH growth and offer the only opportunity to measure MBH beyond the local Universe. However, determining an AGN's host galaxy's stellar velocity dispersion, σå, and its galaxy dynamical mass, Mdyn, is complicated by AGN contamination, aperture effects, and different host-galaxy morphologies. We select a sample of AGNs for which MBH has been independently determined to high accuracy by state-of-the-art techniques: dynamical modeling of the reverberation signal and spatially resolving the broad-line region with the Very Large Telescope Interferometer/GRAVITY. Using integral-field spectroscopic observations, we spatially map the host-galaxy stellar kinematics across the galaxy and bulge effective radii. We find that the dynamically hot component of galaxy disks correlates with MBH; however, the correlations are tightest for aperture-integrated σå measured across the bulge. Accounting for the different MBH distributions, we demonstrate—for the first time—that AGNs follow the same MBH–σ and MBH–M_bulge,dyn relations as quiescent galaxies. We confirm that the classical approach of determining the virial factor as a sample average, yielding log f = 0.65 +/- 0.18, is consistent with the average f from individual measurements. The similarity between the underlying scaling relations of AGNs and quiescent galaxies implies that the current AGN phase is too short to have altered black hole masses on a population level. These results strengthen the local calibration of f for measuring single-epoch MBH in the distant Universe.