Two-dimensional crystals of semiconducting transition metal dichalcogenides absorb a large fraction of incident photons in the visible frequencies despite being atomically thin. It has been suggested that the strong absorption is due to the parallel band or 'band nesting' effect and corresponding divergence in the joint density of states. Here, we use photoluminescence excitation spectroscopy to show that the band nesting in mono- and bilayer MX2 (M=Mo, W and X=S, Se) results in excitation-dependent characteristic relaxation pathways of the photoexcited carriers. Our experimental and simulation results reveal that photoexcited electron-hole pairs in the nesting region spontaneously separate in k-space, relaxing towards immediate band extrema with opposite momentum. These effects imply that the loss of photocarriers due to direct exciton recombination is temporarily suppressed for excitation in resonance with band nesting. Our findings highlight the potential for efficient hot carrier collection using these materials as the absorbers in optoelectronic devices.