Drought and poor soil fertility are among the major abiotic stresses affecting maize productivity in sub-Saharan Africa. Maize breeding efforts at the International Maize and Wheat Improvement Center (CIMMYT) have focused on incorporating drought stress tolerance and nitrogen-use efficiency (NUE) into tropical maize germplasm. The objectives of this study were to estimate the general combining ability (GCA) and specific combining ability (SCA) of selected maize inbred lines under drought stress (DS), low-nitrogen (LN) and optimum moisture and nitrogen (optimum) conditions, and to assess the yield potential and stability of experimental hybrids under these management conditions. Forty-nine experimental three-way cross hybrids, generated from a 7 × 7 line by tester crosses, and six commercial checks were evaluated across 11 optimum, DS and LN sites in Kenya in 2014 using an alpha lattice design with two replicates per entry at each site. DS reduced both grain yield (GY) and plant height (PH), while anthesis–silking interval (ASI) increased under both DS and LN. Hybrids ‘L4/T2’ and ‘L4/T1’ were found to be superior and stable, while inbreds ‘L4’ and ‘L6’ were good combiners for GY and other secondary traits across sites. Additive variance played a greater role for most traits under the three management conditions, suggesting that further progress in the improvement of these traits should be possible. GY under optimum conditions was positively correlated with GY under both DS and LN conditions, but GY under DS and LN was not correlated. Our results suggest the feasibility for simultaneous improvement in grain yield performance of genotypes under optimum, DS and LN conditions.