Based on the framework of an extended multiphase transport model with mean-field potentials in both the partonic phase and the hadronic phase, we explain the elliptic flow difference between π+ and π− in the beam-energy scan program at the relativistic heavy-ion collider by incorporating the vector-isovector potential for quarks and antiquarks with different flavors or isospins. It is found that the isospin splitting of pion elliptic flow favors a strong vector-isovector interaction, and thus serves as a probe of the quark matter equation of state as well as the QCD phase structure at finite baryon and isospin chemical potentials.