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Friction is a dissipative force responsible for conversion of mechanical energy (kinetic & potential) into unwanted heat & sound. Hence, when tyres are properly inflated rolling friction reduces (inflation causes surface area in contact with the ground to decrease thereby reducing friction). And the mechanical energy obtained out of the chemical energy stored in the fuel is not converted to any other form (actually there is some dissipation but we may neglect it). Thus, fuel consumption is reduced in case of inflated tyres.
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Inflation of tires increases their size, hence they cause less friction. When we fill air in tires, it reduces their mass for the smooth running of the vehicle. Hence,the pressure applied on them is reduced and they run efficiently, which reduces fuel consumption.
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