Habitat degradation is the slow--and often subtle--deterioration in habitat quality that accompanies human activities through increases in road density, pesticide use, hunting pressure, etc. Such degradation is of particular concern in fragmented habitats where economic or jurisdictional boundaries rather than ecological ones determine the level of exploitation adjoining habitat patches endure. To examine the consequences habitat degradation might have on species interactions, we posited a patch of pristine habitat surrounded by "matrix" habitat whose degradation level was variable. Using a coupled pair of diffusive Lotka-Volterra competition equations with Robin (mixed) boundary conditions, we modeled the dynamics of two competing species inhabiting the pristine patch and incorporated matrix degradation through a tunable "hostility" parameter representing species' mortality rates in the matrix. We found that the numerical range of competition coefficients over which one species is the competitive dominant and the other inferior may grow or shrink as matrix quality deteriorates. In some cases, degradation of the exterior habitat would bring about a complete competitive reversal inside the preserve. This result, wherein a formerly inferior species supplants a formerly dominant one--even inside the "protected" remnant patch itself--has policy implications for both nature reserve design and management of human activities outside park boundaries.