This paper details the first application of a software tagging algorithm to reduce radon-induced backgrounds in liquid noble element time projection chambers, such as XENON1T and XENONnT. The convection velocity field in XENON1T was mapped out using Rn222 and Po218 events, and the rms convection speed was measured to be 0.30±0.01 cm/s. Given this velocity field, Pb214 background events can be tagged when they are followed by Bi214 and Po214 decays, or preceded by Po218 decays. This was achieved by evolving a point cloud in the direction of a measured convection velocity field, and searching for Bi214 and Po214 decays or Po218 decays within a volume defined by the point cloud. In XENON1T, this tagging system achieved a Pb214 background reduction of 6.2-0.9+0.4% with an exposure loss of 1.8±0.2%, despite the timescales of convection being smaller than the relevant decay times. We show that the performance can be improved in XENONnT, and that the performance of such a software-tagging approach can be expected to be further improved in a diffusion-limited scenario. Finally, a similar method might be useful to tag the cosmogenic Xe137 background, which is relevant to the search for neutrinoless double-beta decay.