Diamonds are erupted at Earth’s surface in volatile-rich magmas called kimberlites1,2,3. These enigmatic magmas, originating from depths exceeding 150 kilometres in Earth’s mantle1, occur in stable cratons and in pulses broadly synchronous with supercontinent cyclicity4. Whether their mobilization is driven by mantle plumes5 or mechanical weakening of cratonic lithosphere4,6 remains unclear. Here we show that most kimberlites spanning the past billion years erupted approximately 25 million years after the onset of continental fragmentation, suggesting an association with rifting processes. Our dynamic models show that physically steep lithosphere-asthenosphere boundaries formed during terminal rifting (necking) generate convective instabilities in the asthenosphere that slowly migrate many hundreds of kilometres inboard of the rift, causing destabilization of cratonic mantle keel tens of kilometres thick. Displaced lithosphere is replaced by hot, upwelling asthenosphere in the return flow, causing partial melting of carbonated mantle and variable assimilation of lithospheric material. The resulting small-volume kimberlite magmas ascend rapidly and adiabatically, exsolving amounts of carbon dioxide (CO2) that are consistent with independent constraints7. Our model reconciles diagnostic kimberlite features including association with cratons and geochemical characteristics that implicate a common asthenospheric mantle source contaminated by cratonic lithosphere8. Together, these results provide a quantitative and mechanistic link between kimberlite episodicity and supercontinent cycles via progressive disruption of cratonic keels.