We introduce a new capability of the Neil Gehrels Swift Observatory, dubbed “continuous commanding,” that achieves 10 s latency response time on orbit to unscheduled target-of-opportunity requests received on the ground. We show that this will allow Swift to respond to premerger (early-warning) gravitational-wave (GW) detections, rapidly slewing the Burst Alert Telescope (BAT) across the sky to place the GW origin in the BAT field of view at or before merger time. This will dramatically increase the GW/gamma-ray burst (GRB) codetection rate and enable prompt arcminute localization of a neutron star merger. We simulate the full Swift response to a GW early-warning alert, including input sky maps produced at different early-warning times, a complete model of the Swift attitude control system, and a full accounting of the latency between the GW detectors and the spacecraft. 60 s of early warning can double the rate of a prompt GRB detection with arcminute localization, and 140 s guarantees observation anywhere on the unocculted sky, even with localization areas ≫1000 deg2. While 140 s is beyond current GW detector sensitivities, 30–70 s is achievable today. We show that the detection yield is now limited by the latency of LIGO/Virgo cyberinfrastructure and motivate a focus on its reduction. Continuous commanding has been integrated as a general capability of Swift, significantly increasing its versatility in response to the growing demands of time-domain astrophysics. We demonstrate this potential on an externally triggered fast radio burst (FRB), slewing 81° across the sky, and collecting X-ray and UV photons from the source position <150 s after the trigger was received from the Canadian Hydrogen Intensity Mapping Experiment, thereby setting the earliest and deepest such constraints on high-energy activity from nonrepeating FRBs. The Swift Team invites the community to consider and propose novel scientific applications of ultra-low-latency UV, X-ray, and gamma-ray observations.