We demonstrate a path to hitherto unachievable differential photometric precisions from the ground, both in the optical and near-infrared (NIR), using custom-fabricated beam-shaping diffusers produced using specialized nanofabrication techniques. Such diffusers mold the focal plane image of a star into a broad and stable top-hat shape, minimizing photometric errors due to non-uniform pixel response, atmospheric seeing effects, imperfect guiding, and telescope-induced variable aberrations seen in defocusing. This PSF reshaping significantly increases the achievable dynamic range of our observations, increasing our observing efficiency and thus better averages over scintillation. Diffusers work in both collimated and converging beams. We present diffuser-assisted optical observations demonstrating 62(-16)(+26) ppm precision in 30 minute bins on a nearby bright star 16 Cygni A (V = 5.95) using the ARC 3.5 m telescope-within a factor of similar to 2 of Kepler's photometric precision on the same star. We also show a transit of WASP-85-Ab (V = 11.2) and TRES-3b (V = 12.4), where the residuals bin down to 180(-41)(+66) ppm in 30 minute bins for WASP-85-Ab-a factor of similar to 4 of the precision achieved by the K2 mission on this target-and to 101 ppm for TRES-3b. In the NIR, where diffusers may provide even more significant improvements over the current state of the art, our preliminary tests demonstrated 137(-36)(+64) ppm precision for a K-S = 10.8 star on the 200 inch. Hale Telescope. These photometric precisions match or surpass the expected photometric precisions of TESS for the same magnitude range. This technology is inexpensive, scalable, easily adaptable, and can have an important and immediate impact on the observations of transits and secondary eclipses of exoplanets.