We present evidence of volcano-tectonic interactions at Sabancaya volcano that we relate to episodic magma injection and high regional fluid pore pressures. We present a surface deformation time series at Sabancaya including observations from ERS-1/2, Envisat, Sentinel-1, COSMO-SkyMed, and TerraSAR-X that spans June 1992 - February 2019. These data show deep seated inflation northwest of Sabancaya from 1992-1997 and 2013-2019, as well as creep and rupture on multiple faults. Afterslip on the Mojopampa fault following a 2013 Mw 5.9 earthquake is anomalously long-lived, continuing for at least six years. The best fit fault plane for the afterslip is right-lateral motion on an EW striking fault at 1 km depth. We also model surface deformation from two 2017 earthquakes (Mw 4.4 and Mw 5.2) on unnamed faults, for which the best fit models are NW striking normal faults at 1-2 km depth. Our best fit model for a magmatic inflation source (13 km depth, volume change of 0.04 to 0.05 km^3 yr^-1), induces positive Coulomb static stress changes on these modeled fault planes. Comparing these deformation results with evidence from satellite thermal and degassing data, field observations, and seismic records, we interpret strong pre-eruptive seismicity at Sabancaya as a consequence of magmatic intrusions destabilizing tectonic faults critically stressed by regionally high fluid pressures. High fluid pressure likely also promotes fault creep driven by static stress transfer from the inflation source. We speculate that strong seismicity near volcanoes will be most likely with high pore fluid pressures and significant, offset magmatic inflation.