We compare the star-forming main sequence (SFMS) of galaxies - both integrated and resolved on 1kpc scales - between the high-resolution TNG50 simulation of IllustrisTNG and observations from the 3D-HST slitless spectroscopic survey at z similar to 1. Contrasting integrated star formation rates (SFRs), we find that the slope and normalization of the star-forming main sequence in TNG50 are quantitatively consistent with values derived by fitting observations from 3D-HST with the Prospector Bayesian inference framework. The previous offsets of 0.2-1 dex between observed and simulated main-sequence normalizations are resolved when using the updated masses and SFRs from Prospector. The scatter is generically smaller in TNG50 than in 3D-HST for more massive galaxies with M-*> 10(10)M(circle dot), by similar to 10-40 per cent, after accounting for observational uncertainties. When comparing resolved star formation, we also find good agreement between TNG50 and 3D-HST: average specific star formation rate (sSFR) radial profiles of galaxies at all masses and radii below, on, and above the SFMS are similar in both normalization and shape. Most noteworthy, massive galaxies with M-*> 10(10.5)M(circle dot), which have fallen below the SFMS due to ongoing quenching, exhibit a clear central SFR suppression, in both TNG50 and 3D-HST. In contrast, the original Illustris simulation and a variant TNG run without black hole kinetic wind feedback, do not reproduce the central SFR profile suppression seen in data. In TNG, inside-out quenching is due to the supermassive black hole (SMBH) feedback model operating at low accretion rates.