Due to feedback from accretion onto supermassive black holes (SMBHs), active galactic nuclei (AGNs) are believed to play a key role in ΛCDM cosmology and galaxy formation. However, AGNs extreme luminosities and the small angular size of their accretion flows create a challenging imaging problem. We show that the James Webb Space Telescope's Near Infrared Imager and Slitless Spectrograph (JWST-NIRISS) Aperture Masking Interferometry (AMI) mode will enable true imaging (i.e., without any requirement of prior assumptions on source geometry) at ∼65 mas angular resolution at the centers of AGNs. This is advantageous for studying complex extended accretion flows around SMBHs and in other areas of angular-resolution-limited astrophysics. By simulating data sequences incorporating expected sources of noise, we demonstrate that JWST-NIRISS AMI mode can map extended structure at a pixel-to-pixel contrast of ∼10 −2 around an L = 7.5 point source, using short exposure times (minutes). Such images will test models of AGN feedback, fueling, and structure (complementary with ALMA observations), and are not currently supported by any ground-based IR interferometer or telescope. Binary point source contrast with NIRISS is ∼10 −4 (for observing binary nuclei in merging galaxies), significantly better than current ground-based optical or IR interferometry. JWST-NIRISS's seven-hole non-redundant mask has a throughput of 15%, and utilizes NIRISS's F277W (2.77 μm), F380M (3.8 μm), F430M (4.3 μm), and F480M (4.8 μm) filters. NIRISS's square pixels are 65 mas per side, with a field of view ∼2 × 2 . We also extrapolate our results to AGN science enabled by non-redundant masking on future 2.4 m and 16 m space telescopes working at long-UV to near-IR wavelengths.