We present a quantitative study of suppression of cold inelastic collisions by the spin-orbit interaction. We prepare cold ensembles of >10(11) Al(2P(1/2)) atoms via cryogenic buffer-gas cooling and use a single-beam optical pumping method to measure their magnetic (m(J)-changing) and fine-structure (J-changing) collisions with 3He atoms at millikelvin temperatures over a range of magnetic fields from 0.5 to 6 T. The experimentally determined rates are in good agreement with the functional form predicted by quantum scattering calculations using ab initio potentials. This comparison provides direct experimental evidence for a proposed model of suppressed inelasticity in collisions of atoms in 2P(1/2) states [T. V. Tscherbul et al., Phys. Rev. A 80, 040701(R) (2009)], which may allow for sympathetic cooling of other 2P(1/2) atoms (e.g., In, Tl and metastable halogens).