High-performance photothermal materials capable of harnessing the entire solar spectrum have garnered significant interest in developing solar-heating sorbents for the effective recovery of viscous oil. Herein, we developed narrow-bandgap MoSe2-loaded reduced graphene oxide (MoSe2-rGO) nanocomposite with efficient solar utilization. MoSe2-rGO with synergistically-enhanced light absorption and photothermal conversion, was first employed for fabricating melamine sponge (MS)-based sorbent (PMGP/MS sorbent) via a facile dip-coating method. The sorbent showed excellent solar-heating capability, reaching a surface temperature of 78 °C in 100 s under 1.0 sun. The sorbent proved effective in recovering highly viscous oil via solar-motivated viscosity-reduction of oil. The sorption rate for viscous crude oil increased 10.6 times under 1.0 sun compared with no sunlight illumination, and the sorption saturation reached around 55.6 g/g within 750 s. Moreover, continuous sorption was achieved under a self-priming pump based on the reduced viscosity and increased fluidity, with capacity of 1.1 g/cm2 at 650 s under 1.0 sun.