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 222Rn and 218Po events, and the rms convection speed was measured to be 0.30±0.01 cm/s. Given this velocity field, 214Pb background events can be tagged when they are followed by 214Bi and 214Po decays, or preceded by 218Po decays. This was achieved by evolving a point cloud in the direction of a measured convection velocity field, and searching for 214Bi and 214Po decays or 218Po decays within a volume defined by the point cloud. In XENON1T, this tagging system achieved a 214Pb background reduction of 6.2+0.4−0.9% 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 137Xe background, which is relevant to the search for neutrinoless double-beta decay.