A direct solvent extraction (DSX) process for purifying nickel and cobalt from the nitric acid leach solution of nickel laterite ores was conceived and experimentally probed. The proposed process consists of two solvent extraction (SX) steps but with only one extractant — bis(2,4,4-trimethylpentyl)phosphinic acid (Cyanex® 272) — used in both steps. The first extraction step involved the removal of aluminum and zinc, whereas the second extraction step involved the separation of cobalt along with manganese from nickel. The experimental results showed essentially quantitative removal of aluminum (>97%) and zinc (>99%) in a single extraction stage using 20vol% Cyanex 272 at pH 2.1. Some cobalt (32%) and manganese (55%) were co-extracted but were easily scrubbed out completely from the loaded organic phase using dilute sulfuric acid at pH ≤ 1.38. Cobalt and manganese in the first extraction raffinate were extracted completely in four extraction stages at staggered pH values of 4.0, 4.4, 4.5, and 4.0 in the first, second, third, and fourth stages, respectively, using also 20vol% Cyanex 272. A small amount of nickel (up to 6.6%) was co-extracted but was easily scrubbed out completely with dilute sulfuric acid at pH 2.0. A flow diagram showing the input and output conditions and the metals separated under the deduced optimum conditions is presented.