Determining the nature of emission processes at the heart of quasars is critical for understanding environments of supermassive black holes. One of the key open questions is the origin of centimetre- to millimetre-wave emission from radio-quiet quasars. The proposed mechanisms range from central star formation to dusty torus, low-power jets, or emission from the accretion-disc corona. Distinguishing between these scenarios requires probing spatial scales of ≤0.01 pc, beyond the reach of any current millimetre-wave telescope. Fortunately, in gravitationally lensed quasars, compact millimetre-wave emission might be microlensed by stars in the foreground galaxy, providing strong constraints on the source size. We report a striking change in rest-frame 1.3 mm flux ratios in RXJ1131−1231, a quadruply lensed quasar at z = 0.658 observed by the Atacama Large Millimeter/submillimeter Array (ALMA) in 2015 and 2020. Over this period, the flux ratios between the three quasar images, A, B, and C, changed by a factor of 1.6 (A/B) and 3.0 (A/C). The observed flux-ratio variability is consistent with the microlensing of a compact source with a half-light radius of ≤50 astronomical units. The compactness of the source leaves coronal emission as the most likely scenario. Furthermore, the inferred millimetre-wave and X-ray luminosities follow the Güdel-Benz relationship for stellar coronae. These observations represent the first unambiguous evidence that coronae are the dominant mechanism for centimetre- to millimetre-wave emission in radio-quiet quasars.