This paper presents a computational study of D+D fusion driven by Coulomb explosion (CE) within a single, homonuclear deuterium nanodroplet, subjected to double-pulse ultraintense laser irradiation. This irradiation scheme results in the attainment (by the first weaker pulse) of a transient inhomogeneous density profile, which serves as a target for the driving (by the second superintense pulse) of nonuniform CE that triggers overrun effects and induces intrananodroplet (INTRA) D+D fusion. Scaled electron and ion dynamics simulations were utilized to explore the INTRA D+D fusion yields for double-pulse, near-infrared laser irradiation of deuterium nanodroplets. The dependence of the INTRA yield on the nanodroplet size and on the parameters of the two laser pulses was determined, establishing the conditions for the prevalence of efficient INTRA fusion. The INTRA fusion yields are amenable to experimental observation within an assembly of nanodroplets. The INTRA D+D fusion can be distinguished from the concurrent internanodroplet D+D fusion reaction occurring in the macroscopic plasma filament and outside it in terms of the different energies of the neutrons produced in these two channels.