Magnetic flux ropes (MFRs) are believed to be at the heart of solar coronal mass ejections (CMEs). A well-known example is the prominence cavity in the low corona that sometimes makes up a three-part white-light (WL) CME upon its eruption. Such a system, which is usually observed in quiet-Sun regions, has long been suggested to be the manifestation of an MFR with relatively cool filament material collecting near its bottom. However, observational evidence of eruptive, filament-hosting MFR systems has been elusive for those originating in active regions. By utilizing multi-passband extreme-ultraviolet (EUV) observations from Solar Dynamics Observatory/Atmospheric Imaging Assembly, we present direct evidence of an eruptive MFR in the low corona that exhibits a hot envelope and a cooler core; the latter is likely the upper part of a filament that undergoes a partial eruption, which is later observed in the upper corona as the coiled kernel of a fast, WL CME. This MFR-like structure exists more than 1 hr prior to its eruption, and displays successive stages of dynamical evolution, in which both ideal and non-ideal physical processes may be involved. The timing of the MFR kinematics is found to be well correlated with the energy release of the associated long-duration C1.9 flare. We suggest that the long-duration flare is the result of prolonged energy release associated with the vertical current sheet induced by the erupting MFR.