We report wind measurements within Martian dust devils observed in plan view from the High Resolution Imaging Science Experiment (HiRISE) orbiting Mars. The central color swath of the HiRISE instrument has three separate charge‐coupled devices (CCDs) and color filters that observe the surface in rapid cadence. Active features, such as dust devils, appear in motion when observed by this region of the instrument. Our image animations reveal clear circulatory motion within dust devils that is separate from their translational motion across the Martian surface. Both manual and automated tracking of dust devil clouds reveal tangential winds that approach 20–30 m s⁻¹ in some cases. These winds are sufficient to induce a ∼1% decrease in atmospheric pressure within the dust devil core relative to ambient, facilitating dust lifting by reducing the threshold wind speed for particle elevation. Finally, radial velocity profiles constructed from our automated measurements test the Rankine vortex model for dust devil structure. Our profiles successfully reveal the solid body rotation component in the interior, but fail to conclusively illuminate the profile in the outer regions of the vortex. One profile provides evidence for a velocity decrease as a function of r^−1/2, instead of r⁻¹, suggestive of surface friction effects. However, other profiles do not support this observation, or do not contain enough measurements to produce meaningful insights.