We present constraints on the equation of state of dark energy, w, and the total matter density, Ω M , derived from the double-source-plane strong lens SDSSJ0946+1006, the first cosmological measurement with a galaxy-scale doublesource-plane lens. By modelling the primary lens with an elliptical power-law mass distribution, and including perturbative lensing by the first source, we are able to constrain the cosmological scaling factor in this system to be β −1 = 1.404 ± 0.016, which implies Ω M = 0.33 +0.33 −0.26 for a flat ΛCDM cosmology. Combining with a CMB prior from Planck, we find w = −1.17 +0.20 −0.21 assuming a flat wCDM cosmology. This inference shifts the posterior by 1σ and improves the precision by 30 per cent with respect to Planck alone, and demonstrates the utility of combining simple, galaxy-scale multiple-source-plane lenses with other cosmological probes to improve precision and test for residual systematic biases.