Block polymers offer unparalleled opportunities for designing materials with enhanced functionalities and properties. Hence, we report a synthetic strategy for diblock polyesters through bridging two distinct reactions between ring-opening polymerization of lactide (LA) and ring-opening copolymerization of epoxides with anhydrides by using a binary catalyst. Specifically, in the terpolymerization of LA, epichlorohydrin (ECH), and phthalic anhydride (PA), spectroscopy indicated that this process occurs first by ECH/PA copolymerization and then homopolymerization of LA, forming diblock polyester. Density functional theory (DFT) calculations revealed that coupling of ECH/PA was more favorable than LA homopolymerization in the presence of PA, while an incorporation of LA into the ECH-PA sequence was also possible owing to the competitive energy barriers and thermodynamic priority. It was also computationally found that LA homopolymerization occurred after consumption of PA to achieve diblock polyester, as experimentally observed. Furthermore, the diblock polyester architectures could be extended and modified by introducing various monomers.