High-quality single-layer dispersions have long been a critical prerequisite for fabricating uniform monolayer coatings of two-dimensional (2D) materials, which unfortunately demand extensive processing steps such as iterative exfoliation and exhaustive purification. Here, using graphene oxide (GO) as the first prototypical 2D material, we demonstrate a "stick-and-tear" strategy to rapidly produce near-complete, precisely single-layer coatings on diverse substrates directly from crude GO suspensions, which contain heterogeneous structures and aggregates of various geometries and ionic impurities. In the "stick" step, only the soft, compliant components of the unpurified crude suspension (e.g., few- and single-layer sheets or loose aggregates) can conform to and strongly adhere to the substrate. During the subsequent "tear" step, excess layers, wrinkles, and overlapping regions are selectively removed by gentle sonication. It is demonstrated that the process works over a broad range of GO concentrations, solution pH values, and can tolerate salt concentrations well above the maximal levels of typical GO synthesis. Monolayer coatings on SiO2/Si, glass, indium-tin oxide (ITO)/glass, and curved metal surfaces have been demonstrated. As a proof-of-concept of potential uses, such precise monolayer coating of GO is demonstrated to be an effective hole-transport-layer on ITO for high-performance organic photovoltaic devices. The strategy's material-agnostic nature is further validated by producing dense monolayer coatings of Ti3C2Tx MXene directly from its crude suspensions. By leveraging inherent mechanical contrasts in 2D materials, this work establishes a rapid, scalable pathway to precise monolayer coatings, circumventing conventional purification bottlenecks and opening avenues for functional devices with diverse colloidal 2D materials.