Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) is a promising bio-based and biodegradable thermoplastic with restricted industrial applications due to its brittleness and poor processability. Natural rubber (NR) has been used as a toughening agent, but further physical improvements are desired. In this study, rubber toughening efficiency was significantly improved through the synergistic use of a trifunctional acrylic coagent and an organic peroxide during reactive extrusion of PHBV and NR. The rheological, crystallization, thermal, morphological, and mechanical properties of PHBV/NR blends with 15% rubber loading were characterized. The peroxide and coagent synergistically crosslinked the rubber phase and grafted PHBV onto rubber backbones, leading to enhanced rubber modulus and cohesive strength as well as improved PHBV–rubber compatibility and blend homogeneity. Simultaneously, the peroxide–coagent treatment decreased PHBV crystallinity and crystal size and depressed peroxy-radical-caused PHBV degradation. The new PHBV/NR blends had a broader processing window, 75% better toughness (based on the notched impact strength data), and 100% better ductility (based on the tensile elongation data) than pristine PHBV. This new rubber-toughened PHBV material has balanced mechanical performance comparable to that of conventional thermoplastics and is suitable for a wide range of plastic applications.