Context : Aims : We present the first three-dimensional internal motions for individual stars in the Draco dwarf spheroidal galaxy . Methods : By combining first-epoch Hubble Space Telescope observations and second-epoch Gaia Data Release 2 positions , we measured the proper motions of 149 sources in the direction of Draco . We determined the line-of-sight velocities for a sub-sample of 81 red giant branch stars using medium resolution spectra acquired with the DEIMOS spectrograph at the Keck II telescope . Altogether , this resulted in a final sample of 45 Draco members with high-precision and accurate 3D motions , which we present as a table in this paper . Results : Based on this high-quality dataset , we determined the velocity dispersions at a projected distance of \sim 120 pc from the centre of Draco to be \sigma _ { R } = 11.0 ^ { +2.1 } _ { -1.5 } km/s , \sigma _ { T } = 9.9 ^ { +2.3 } _ { -3.1 } km/s and \sigma _ { LOS } = 9.0 ^ { +1.1 } _ { -1.1 } km/s in the projected radial , tangential , and line-of-sight directions . This results in a velocity anisotropy \beta = 0.25 ^ { +0.47 } _ { -1.38 } at r \gtrsim 120 pc . Tighter constraints may be obtained using the spherical Jeans equations and assuming constant anisotropy and Navarro-Frenk-White ( NFW ) mass profiles , also based on the assumption that the 3D velocity dispersion should be lower than \approx 1 / 3 of the escape velocity of the system . In this case , we constrain the maximum circular velocity V _ { max } of Draco to be in the range of 10.2 - 17.0 km/s . The corresponding mass range is in good agreement with previous estimates based on line-of-sight velocities only . Conclusions : Our Jeans modelling supports the case for a cuspy dark matter profile in this galaxy . Firmer conclusions may be drawn by applying more sophisticated models to this dataset and with new datasets from upcoming Gaia releases .