When a hydrogen (H) atom approaches a deuterium (D-2) molecule, the minimum-energy path is for the three nuclei to line up. Consequently, nearly collinear collisions cause HD reaction products to be backscattered with low rotational excitation, whereas more glancing collisions yield sideways-scattered HD products with higher rotational excitation. Here we report that measured cross sections for the H + D-2 -> HD(v' = 4, j') + D reaction at a collision energy of 1.97 electron volts contradict this behavior. The anomalous angular distributions match closely fully quantum mechanical calculations, and for the most part quasiclassical trajectory calculations. As the energy available in product recoil is reduced, a rotational barrier to reaction cuts off contributions from glancing collisions, causing high-j' HD products to become backward scattered.