In this paper, the classical linear tuned mass damper (TMD) is coupled with an inerter, a two-terminal device resisting the relative acceleration of its terminals, in various tuned mass-damper-inerter (TMDI) topologies to suppress excessive wind-induced oscillations in tall buildings causing occupant discomfort. A parametric numerical study is undertaken involving a top-floor-TMD-equipped planar frame accurately capturing the in-plane dynamic behavior of a 74-story benchmark building exposed to a quasi-stationary spatially correlated wind-force field accounting for vortex shedding effects in the across-wind direction. It is found that the TMDI reduces peak top-floor acceleration more effectively than the TMD by considering smaller attached-mass values, and TMDI topologies in which the inerter spans more stories in linking the attached mass to the host structure. Moreover, the inclusion of the inerter dramatically reduces the TMD stroke, and it has been verified that the magnitude of the developing inerter forces can be readily accommodated by the host structure. Pertinent illustrative examples are included showcasing that the TMDI meets code-prescribed serviceability design requirements for new tall buildings using significantly smaller attached mass compared with the TMD, and that inerter devices can be used to upgrade the performance of existing TMD-equipped tall buildings without changing the attached mass.