Monolayer two-dimensional (2D) materials have promising optical properties and hold potential as solar absorbers for photovoltaic devices. Efficient solar absorbers should have high absorption especially for wavelengths slightly smaller than the semiconductor bandgap wavelength. In this spectrum, solar cells have higher internal quantum efficiency, lower energy loss to lattice vibration, and resultant higher power conversion efficiency. 2D materials have been integrated into nanophotonic structures to enhance their absorption, but fabrication challenges hindered practical applications of these structures. Here, we theoretically and experimentally demonstrated a simple methodology to design efficient 2D material, and more generally, sub-nanometer planar, optical absorbers by placing a sub-nanometer film either onto a transparent layer on a metallic film substrate (structure 1) or between the transparent layer and the substrate (structure 2) with oblique sunlight illumination. We show that there always exist a pair of transparent layer thickness and incident angle for which these structures achieve 100% absorption (broadband and angle -robust absorption for structure 1 and narrowband for structure 2). 92% absorption, which is 2.6 times greater than prior theoretical demonstrations, was achieved in monolayer MoS2 at 660 nm near its band edge to demonstrate material versatility (even materials with very low losses, which is counter-intuitive to conventional absorber designs). 2D material solar cells were further designed with 4.4% power conversion efficiency, a four-fold increase compared to prior designs. Our proposed methodology is applicable to numerous materials with atomic-layer or sub-nanometer thicknesses and paves the way to efficient sub-nanometer-thick energy harvesting devices with simple planar structures.