The expansion of rubber cultivation into drought prone areas calls for innovative management to increase the drought resistance of the trees. The competition for water exerted by an intercrop in the upper soil layers will likely stimulate the growth of young rubber tree roots into deeper soil layers where water availability is more stable. This study examined the effects of a legume (Pueraria phaseoloides) and a grass (Vetiveria zizanoides) intercrop, on the fine root traits of young rubber trees (Hevea brasiliensis Müll. Arg.) established along a toposequence covering a range of soil depths in northeast Thailand. Two plots with and without the intercrops were set up in a 3-year-old rubber plantation. Tree girth, mortality rate, nutrient content in the leaves, predawn leaf water potential, and soil water content profiles were monitored over four successive years. Fine root length density, specific root length, fine root biomass, and fine root diameter of the rubber trees were measured in the fourth year. In shallow soils, the trees with the legume intercrop had a higher growth rate, a higher leaf nutrient content, and a higher fine root length density in the deepest soil layers than the controls, supporting the hypothesis of an adaptive root response, increasing drought resistance. However, the trees with the grass intercrop did not show this effect. In deep soils, specific root length was highest without the intercrops, and the soil water profile and predawn leaf water potential suggested that trees with intercrops benefited from increased water extraction below 110 cm depth. We showed, for the first time, that rubber tree root traits can be manipulated through intercropping to improve drought resistance. However, our results suggest intercropping might not reduce risks of tree mortality caused by drought in the shallowest soils of the subhumid area of northeast Thailand.