The structural geometry of transfer and accommodation zones that relay strain between extensional domains in rifted crust has been addressed in many studies over the past 30 years. However, details of the kinematics of deformation and related stress changes within these zones have received relatively little attention. In this study we conduct the first-ever systematic, multi-basin fault-slip measurement campaign within the late Cenozoic Rio Grande rift of northern New Mexico to address the mechanisms and causes of extensional strain transfer associated with a broad accommodation zone. Numerous (562) kinematic measurements were collected at fault exposures within and adjacent to the NE-trending Santo Domingo Basin accommodation zone, or relay, which structurally links the N-trending, right-stepping en echelon Albuquerque and Española rift basins. The following observations are made based on these fault measurements and paleostresses computed from them. (1) Compared to the typical northerly striking normal to normal-oblique faults in the rift basins to the north and south, normal-oblique faults are broadly distributed within two merging, NE-trending zones on the northwest and southeast sides of the Santo Domingo Basin. (2) Faults in these zones have greater dispersion of rake values and fault strikes, greater dextral strike-slip components over a wide northerly strike range, and small to moderate clockwise deflections of their tips. (3) Relative-age relations among fault surfaces and slickenlines used to compute reduced stress tensors suggest that far-field, ~E-W–trending σ₃ stress trajectories were perturbed 45° to 90° clockwise into NW to N trends within the Santo Domingo zones. (4) Fault-stratigraphic age relations constrain the stress perturbations to the later stages of rifting, possibly as late as 2.7–1.1 Ma. Our fault observations and previous paleomagnetic evidence of post–2.7 Ma counterclockwise vertical-axis rotations are consistent with increased bulk sinistral-normal oblique shear along the Santo Domingo rift segment in Pliocene and later time. Regional geologic evidence suggests that the width of active rift faulting became increasingly confined to the Santo Domingo Basin and axial parts of the adjoining basins beginning in the late Miocene. We infer that the Santo Domingo clockwise stress perturbations developed coevally with the oblique rift segment mainly due to mechanical interactions of large faults propagating toward each other from the adjoining basins as the rift narrowed. Our results suggest that negligible bulk strike-slip displacement has been accommodated along the north-trending rift during much of its development, but uncertainties in the maximum ages of fault slip do not allow us to fully evaluate and discriminate between earlier models that invoked northward or southward rotation and translation of the Colorado Plateau during early (Miocene) rifting.