Intercropping, which grows at least two crop species on the same pieces of land at the same time, can increase grain yields greatly. Legume-grass intercrops are known to overyield because of legume nitrogen fixation. However, many agricultural soils are deficient in phosphorus. Here we show that a new mechanism of overyielding, in which phosphorus mobilized by one crop species increases the growth of a second crop species grown in alternate rows, led to large yield increases on phosphorus-deficient soils. In 4 years of field experiments, maize (Zea mays L.) overyielded by 43% and faba bean (Vicia faba L.) overyielded by 26% when intercropped on a low-phosphorus but high-nitrogen soil. We found that overyielding of maize was attributable to below-ground interactions between faba bean and maize in another field experiment. Intercropping with faba bean improved maize grain yield significantly and above-ground biomass marginally significantly, compared with maize grown with wheat, at lower rates of P fertilizer application (<75 kg of P ₂O₅ per hectare), and not significantly at high rate of P application (>112.5 kg of P₂O₅ per hectare). By using permeable and impermeable root barriers, we found that maize overyielding resulted from its uptake of phosphorus mobilized by the acidification of the rhizosphere via faba bean root release of organic acids and protons. Faba bean overyielded because its growth season and rooting depth differed from maize. The large increase in yields from intercropping on low-phosphorus soils is likely to be especially important on heavily weathered soils.