ABSTRACT We report detection of a very bright X-ray–UV–optical outburst of OJ 287 in 2020 April–June, the second brightest since the beginning of our Swift multiyear monitoring in late 2015. It is shown that the outburst is predominantly powered by jet emission. Optical–UV–X-rays are closely correlated, and the low-energy part of the XMM–Newton spectrum displays an exceptionally soft emission component consistent with a synchrotron origin. A much harder X-ray power-law component (Γx = 2.4, still relatively steep when compared to expectations from inverse Compton models) is detected out to 70 keV by NuSTAR. We find evidence for reprocessing around the Fe region, consistent with an absorption line. If confirmed, it implies matter in outflow at ∼0.1c. The multiyear Swift light curve shows multiple episodes of flaring or dipping with a total amplitude of variability of a factor of 10 in X-rays, and 15 in the optical–UV. The 2020 outburst observations are consistent with an after-flare predicted by the binary black hole model of OJ 287, where the disc impact of the secondary black hole triggers time-delayed accretion and jet activity of the primary black hole.