The geographic rearrangement of the tropical oceanic and atmospheric circulation during an El Niño event is associated with a well-understood strong surface warming of the climatologically cold eastern equatorial Pacific. However, the concomitant warming of the warmest waters where deep convection occurs - responsible for the tropics-wide free tropospheric warming- is less well understood. Here, we show that in both a coupled atmosphere-ocean climate model and in reanalysis data, El Niño is associated with an increase in evaporation over the colder ~70%, but with a decrease in evaporation over the warmest ~30% of the tropical oceans where atmospheric deep convection connects the surface with the free troposphere. The reduction in evaporation is driven by a weakening of the near-surface winds. We propose that the prominent tropics-wide warming during El Niño is a consequence of the reduction of near-surface winds in regions of deep convection due to the anomalous large-scale circulation.