Drowned carbonate reefs on passive margins are puzzling because of their enormous growth potential compared to typical rates of passive margin subsidence and moderate sea-level fluctuations. A possible solution to this paradox is that slow processes acting over geologic time weaken reefs and contribute to their ultimate demise. The Australian northeastern marginal plateaus, known for their drowned reefs, underwent a period of accelerated tectonic subsidence during the late Miocene to Pliocene that, combined with a sequence of second-order global sea-level rises, outpaced reef growth and drowned the once-thriving Miocene carbonate platforms. However, the mechanism for the observed anomalous subsidence of this relatively mature passive margin 1000 km from the nearest plate boundary is uncertain. We use a coupled plate, kinematic mantle flow model to show that in the late Miocene northeastern Australia overrode subducted slabs from Eocene Melanesian subduction north of Papua New Guinea. We find that the rate of surface subsidence induced by the sinking slabs increases the likelihood that relative sea-level rises outpaced late Miocene reef growth. In addition to the well-known effects of long-term plate processes and short-term global sea-level and climate change, our results demonstrate that deep Earth processes can play a substantial role in driving the evolution of passive margins and coral reefs.