Mounting theoretical evidence suggests that demographic stochasticity, environmental heterogeneity and biased movement of organisms individually affect the dynamics of biological invasions and range expansions. Studies of species spread in heterogeneous landscapes have traditionally characterized invasion velocities as functions of the mean resource density throughout the landscape, thus neglecting higher-order moments of the spatial resource distribution. Here, we show theoretically that different spatial arrangements of resources lead to different spread velocities even if the mean resource density throughout the landscape is kept constant. Specifically, we find that increasing the resource autocorrelation length causes a reduction in the speed of species spread. The model shows that demographic stochasticity plays a key role in the slowdown, which is strengthened when individuals can actively move towards resources. We then experimentally corroborated the theoretically predicted reduction in propagation speed in microcosm experiments with the protist Euglena gracilis by comparing spread in landscapes with different resource autocorrelation lengths. Our work identifies the resource autocorrelation length as a key modulator and a simple measure of landscape susceptibility to biological invasions, which needs to be considered for predicting invasion dynamics within naturally heterogeneous environmental corridors.