In shallow aquatic systems benthic and pelagic primary producers typically compete for light and nutrients along opposing vertical supply axes pelagic algae shade the benthic habitat; conversely, benthic algae intercept the nutrient flux from the sediment to the pelagic habitat. We present a general framework for analyzing such spatially asymmetric resource competition across habitat boundaries using a mechanistic, dynamical model. We visualize the mechanisms determining the outcome of these cross-habitat interactions using zero-net-growth-isoclines, resource supply points, and resource consumption vectors. In extensive invasion analyses we characterize the abiotic and competitive persistence boundaries of pelagic and benthic primary producers, which are set by environmental factors determining nutrient and light supply and are modified by resource use by the competitor in the respective other habitat. We note several qualitative differences between cross-habitat and 'classical' within-habitat resource competition. First, coexistence of cross-habitat competitors is facilitated by, but does not require niche differentiation with respect to the utilization of resources. Because each species has a competitive edge for the resource that is supplied from 'its' side of the system, a competitor which is inferior in utilizing both resources can sometimes coexist with - or even exclude - a superior competitor. Second, increasing the external supply of one resource (the nutrient) may initially favor both competitors - until a breakpoint is reached where the benthic producer goes abruptly extinct. Finally, whether a given pair of cross-habitat competitors coexist or shows alternative states may depend on the environment. Specifically, benthic and pelagic algae may coexist at low nutrient and light supply but produce alternative states at high nutrient and light supply. Alternative states are, in turn, promoted by any algal trait combination that increases the spatial asymmetry in resource consumption, i.e. leads to a higher nutrient consumption in the benthic habitat and/or a higher light consumption in the pelagic habitat. In a first empirical application we show that predictions from our model give a good fit to published data on benthic and pelagic primary production in temperate and arctic lakes spanning a broad range of nutrient environments.