The tight correlation between total galaxy stellar mass and star formation rate (SFR) has become known as the star-forming main sequence. Using ∼487 000 spaxels from galaxies observed as part of the Sloan Digital Sky Survey Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, we confirm previous results that a correlation also exists between the surface densities of star formation (Σ_SFR) and stellar mass (Σ_⋆) on kpc scales, representing a ‘resolved’ main sequence. Using a new metric (ΔΣ_SFR), which measures the relative enhancement or deficit of star formation on a spaxel-by-spaxel basis relative to the resolved main sequence, we investigate the SFR profiles of 864 galaxies as a function of their position relative to the global star-forming main sequence (ΔSFR). For galaxies above the global main sequence (positive ΔSFR) ΔΣ_SFR is elevated throughout the galaxy, but the greatest enhancement in star formation occurs at small radii (<3 kpc, or 0.5R_e). Moreover, galaxies that are at least a factor of 3 above the main sequence show diluted gas phase metallicities out to 2R_e, indicative of metal-poor gas inflows accompanying the starbursts. For quiescent/passive galaxies that lie at least a factor of 10 below the star-forming main sequence, there is an analogous deficit of star formation throughout the galaxy with the lowest values of ΔΣ_SFR in the central 3 kpc. Our results are in qualitative agreement with the ‘compaction’ scenario in which a central starburst leads to mass growth in the bulge and may ultimately precede galactic quenching from the inside-out.