Super-rotation affects - and is affected by - the distribution of dust in the martian atmosphere. We modelled this interaction during the 2018 global dust storm (GDS) of Mars Year 34 using data assimilation. Super-rotation increased by a factor of two at the peak of the GDS, as compared to the same period in the previous year which did not feature a GDS. A strong westerly jet formed in the tropical lower atmosphere, with strong easterlies above 60 km, as a result of momentum transport by thermal tides. Enhanced super-rotation is shown to have commenced 40 sols before the onset of the GDS, due to equatorward advection of dust from southern mid-latitudes. The uniform distribution of dust in the tropics resulted in a symmetric Hadley cell with a tropical upwelling branch that could efficiently transport dust vertically; this may have significantly contributed to the rapid expansion of the storm.