Using Monte Carlo simulations, we investigate the self-assembly of model nanoparticles inside a matrix of model equilibrium polymers (or matrix of wormlike micelles) as a function of the polymeric matrix density and the excluded volume parameter between polymers and nanoparticles. In this paper, we show morphological transitions in the system architecture via synergistic self-assembly of nanoparticles and the equilibrium polymers. In a synergistic self-assembly, the resulting morphology of the system is a result of the interaction between the nanoparticles and the polymers and corresponding re-organization of both the assemblies. This is different from the polymer templating method. We report the morphological transition of nanoparticle aggregates from percolating network-like structures to non-percolating clusters as a result of the change in the excluded volume parameter between nanoparticles and polymeric chains. Corresponding to the change in the self-assembled structures of nanoparticles, the matrix of equilibrium polymers also simultaneously shows a transition from a dispersed state to a percolating network-like structure formed by the clusters of polymeric chains. We show that the shape anisotropy of the nanoparticle clusters formed is governed by the polymeric density resulting in rod-like, sheet-like or other anisotropic nanoclusters. It is also shown that the pore shape and the pore size of the porous network of nanoparticles can be changed by changing the minimum approaching distance between nanoparticles and polymers. We provide a theoretical understanding of why various nanostructures with very different morphologies are obtained.