The β-decay half-lives of 94 neutron-rich nuclei ^{144-151}Cs, ^{146-154}Ba, ^{148-156}La, ^{150-158}Ce, ^{153-160}Pr, ^{156-162}Nd, ^{159-163}Pm, ^{160-166}Sm, ^{161-168}Eu, ^{165-170}Gd, ^{166-172}Tb, ^{169-173}Dy, ^{172-175}Ho, and two isomeric states ^{174m}Er, ^{172m}Dy were measured at the Radioactive Isotope Beam Factory, providing a new experimental basis to test theoretical models. Strikingly large drops of β-decay half-lives are observed at neutron-number N=97 for _{58}Ce, _{59}Pr, _{60}Nd, and _{62}Sm, and N=105 for _{63}Eu, _{64}Gd, _{65}Tb, and _{66}Dy. Features in the data mirror the interplay between pairing effects and microscopic structure. r-process network calculations performed for a range of mass models and astrophysical conditions show that the 57 half-lives measured for the first time play an important role in shaping the abundance pattern of rare-earth elements in the solar system.