The β-decay half-lives of neutron-rich nuclei with 20≤Z≤50 are systematically investigated using the newly developed fully self-consistent proton–neutron quasiparticle random phase approximation (QRPA), based on the spherical relativistic Hartree–Fock–Bogoliubov (RHFB) framework. Available data are reproduced by including an isospin-dependent proton–neutron pairing interaction in the isoscalar channel of the RHFB+QRPA model. With the calculated β-decay half-lives of neutron-rich nuclei a remarkable speeding up of r-matter flow is predicted. This leads to enhanced r-process abundances of elements with A≳140, an important result for the understanding of the origin of heavy elements in the universe.