It is well-known that the Dengue fever virus undergoes a distinct morphological transition from topologically smooth particles to ‘bumpy’ particle on increasing the temperature from that of the mosquito carrier (28 °C) to that of the human host (37 °C). This virus also possesses pH-sensitive surface domains that undergo conformational changes during infection which facilitates exit from the endosomes. Herein we take a bio-inspired approach to design synthetic Dengue virus-mimicking nanoparticles to target triple-negative (TN) breast cancer cells that overexpress SR-B1 scavenger receptors. Thus, sterile pH-responsive methacrylic ABC triblock copolymer vesicles were prepared in aqueous solution via polymerization-induced self-assembly. Microphase separation between two enthalpically-incompatible hydrophobic membrane-forming blocks produced a well-defined framboidal morphology, with surface globules of ∼28 nm diameter protruding from the membrane. The hydrophilic stabilizer block comprises 97% hydroxyl-functionalized chains and 3% phosphorylcholine-functionalized chains, with the latter being critical for selective intracellular uptake. These framboidal vesicles remain intact at neutral pH but become swollen and cationic at pH 5–6 because the tertiary amine residues in the hydrophobic C block become protonated. We demonstrate that such nanoparticles enable selective targeting of TN breast cancer cells. This is because such malignant cells overexpress SR-B1 receptors for naturally-occurring phospholipids and hence take up the phosphorylcholine-decorated framboidal vesicles preferentially. In contrast, negligible cell uptake is observed over the same time period for both human dermal fibroblasts and normal breast cancer cells that minimally express the SR-B1 receptor. Moreover, we show that genetic material within such pH-responsive framboidal vesicles can be efficiently delivered to the cell nuclei while maintaining high cell viability.