Determining the oxygen fugacity of Earth's silicate mantle is of prime importance because it affects the speciation and mobility of volatile elements in the interior and has controlled the character of degassing species from the Earth since the planet's formation. Oxygen fugacities recorded by garnet-bearing peridotite xenoliths from Archaean lithosphere are of particular interest, because they provide constraints on the nature of volatile-bearing metasomatic fluids and melts active in the oldest mantle samples, including those in which diamonds are found. Here we report the results of experiments to test garnet oxythermobarometry equilibria under high-pressure conditions relevant to the deepest mantle xenoliths. We present a formulation for the most successful equilibrium and use it to determine an accurate picture of the oxygen fugacity through cratonic lithosphere. The oxygen fugacity of the deepest rocks is found to be at least one order of magnitude more oxidized than previously estimated. At depths where diamonds can form, the oxygen fugacity is not compatible with the stability of either carbonate- or methane-rich liquid but is instead compatible with a metasomatic liquid poor in carbonate and dominated by either water or silicate melt. The equilibrium also indicates that the relative oxygen fugacity of garnet-bearing rocks will increase with decreasing depth during adiabatic decompression. This implies that carbon in the asthenospheric mantle will be hosted as graphite or diamond but will be oxidized to produce carbonate melt through the reduction of Fe(3+) in silicate minerals during upwelling. The depth of carbonate melt formation will depend on the ratio of Fe(3+) to total iron in the bulk rock. This 'redox melting' relationship has important implications for the onset of geophysically detectable incipient melting and for the extraction of carbon dioxide from the mantle through decompressive melting.