Many governments have managed to control their COVID-19 outbreak with a simple message: keep the effective '$R$ number' $R<1$ to prevent widespread contagion and flatten the curve. This raises the question whether a similar policy could control dangerous online 'infodemics' of information, misinformation and disinformation. Here we show, using multi-platform data from the COVID-19 infodemic, that its online spreading instead encompasses a different dynamical regime where communities and users within and across independent platforms, sporadically form temporary active links on similar timescales to the viral spreading. This allows material that might have died out, to evolve and even mutate. This has enabled niche networks that were already successfully spreading hate and anti-vaccination material, to rapidly become global super-spreaders of narratives featuring fake COVID-19 treatments, anti-Asian sentiment and conspiracy theories. We derive new tools that incorporate these coupled social-viral dynamics, including an online $R$, to help prevent infodemic spreading at all scales: from spreading across platforms (e.g. Facebook, 4Chan) to spreading within a given subpopulation, or community, or topic. By accounting for similar social and viral timescales, the same mathematical theory also offers a quantitative description of other unconventional infection profiles such as rumors spreading in financial markets and colds spreading in schools.