Core–shell nanostructures are powerful platforms for the development of novel nanoscale drug delivery systems with sustained drug release profiles. Coaxial electrospinning is facile and convenient for creating medicated core–shell nanostructures with elaborate designs with which the sustained-release behaviors of drug molecules can be intentionally adjusted. With resveratrol (RES) as a model for a poorly water-soluble drug and cellulose acetate (CA) and PVP as polymeric carriers, a brand-new electrospun core–shell nanostructure was fabricated in this study. The guest RES and the host CA molecules were designed to have a reverse gradient distribution within the core–shell nanostructures. Scanning electron microscope and transmission electron microscope evaluations verified that these nanofibers had linear morphologies, without beads or spindles, and an obvious core–shell double-chamber structure. The X-ray diffraction patterns and Fourier transform infrared spectroscopic results indicated that the involved components were highly compatible and presented in an amorphous molecular distribution state. In vitro dissolution tests verified that the new core–shell structures were able to prevent the initial burst release, extend the continuous-release time period, and reduce the negative tailing-off release effect, thus ensuring a better sustained-release profile than the traditional blended drug-loaded nanofibers. The mechanism underlying the influence of the new core–shell structure with an RES/CA reverse gradient distribution on the behaviors of RES release is proposed. Based on this proof-of-concept demonstration, a series of advanced functional nanomaterials can be similarly developed based on the gradient distributions of functional molecules within electrospun multi-chamber nanostructures.