Understanding the crustal fault interaction and connection between earthquakes in areas with slow tectonic deformation, such as Betic Cordillera (South Spain), is challenging. When seismic rates are low and large destructive earthquakes happen less frequently, it is necessary to resort to historical or paleoseismic records. This study investigates the postseismic viscoelastic relaxation mechanism as a potential explanation for the occurrence of three historical earthquakes (IEMSVIII‐IX) in the Eastern Betic Shear Zone during the XVI‐century, all of which occurred within a span of 13 years: 1518 Vera Mw6.2, 1522 Alhama de Almeria Mw6.5, and 1531 Baza Mw6.2 associated with the Palomares, Carboneras, and Baza faults, respectively. The results strongly suggest a sequential stress‐triggering connection between the three events. The northern NS‐oriented section of the Baza fault is found to have experienced a larger positive ΔCFS and, indeed, more prone to rupture in 1531. The study also examines whether the cumulative ΔCFS had influenced the occurrence of further significant earthquakes (≥Mw6.0) in the region. A triggering connection between the cascade and the 1658 Almeria Mw6.2 earthquake is suggested, whereas no indications of similar linkage to the 1674 Lorca Mw6.0 or the 1804 Dalias Mw6.4 events are found. The stress triggering impact of the cascade over nearby active faults is noteworthy. It is expected that this analysis could have future applications for studying other important historical events, and improving seismic hazard analysis in complex fault settings of the Betic Cordillera.