Convectively coupled Kelvin waves (CCKWs) are tropical weather systems that travel eastward along the equatorial waveguide and have previously been linked to 90% of flooding events in Sumatra, Indonesia. Here, the processes through which CCKWs influence convection to produce extreme precipitation are investigated, with a focus on Padang, a city on the west coast of Sumatra. Extreme precipitation days at Padang, defined as days when the daily total precipitation exceeds the percentile, are found to be 59% more likely to occur given the presence of a CCKW. We find that CCKWs modulate the diurnal cycle to produce extreme precipitation. This is achieved firstly through providing low‐level moisture and convergence that acts to couple the Kelvin wave to the convection. Secondly, the CCKW acts to displace the convergence zone towards Padang, such that it experiences rainfall that persists throughout the night and peaks the following day in the early evening. We examine the case study of a CCKW that passed over Padang on August 21, 2017, bringing extreme precipitation that led to flooding in the West Sumatra region, recording a maximum daily accumulated rainfall of 137 mm. This case study showed remarkably similar characteristics in its propagation, structure, and precipitation patterns to composite studies of CCKWs. The performance of a suite of convection‐permitting configurations of the UK Met Office Unified Model (MetUM), embedded within a parameterised convection global model, in forecasting this CCKW is evaluated. In general, all configurations of the model capture this event reasonably well. We find that extending the western boundary of the high‐resolution model domain from 90°E to 65°E leads to a significantly improved forecast, as the CCKW development over the Indian Ocean is captured more accurately by the high‐resolution nested model, compared with the lower‐resolution global driving model.