We present a broadband X-ray study of W50 (the “Manatee” nebula), the complex region powered by the microquasar SS 433, that provides a test bed for several important astrophysical processes. The W50 nebula, a Galactic PeVatron candidate, is classified as a supernova remnant but has an unusual double-lobed morphology likely associated with the jets from SS 433. Using NuSTAR, XMM-Newton, and Chandra observations of the inner eastern lobe of W50, we have detected hard nonthermal X-ray emission up to ∼30 keV, originating from a few-arcminute-sized knotty region (“Head”) located ≲18′ (29 pc for a distance of 5.5 kpc) east of SS 433, and constrained its photon index to 1.58 ± 0.05 (0.5–30 keV band). The index gradually steepens eastward out to the radio “ear” where thermal soft X-ray emission with a temperature kT ∼ 0.2 keV dominates. The hard X-ray knots mark the location of acceleration sites within the jet and require an equipartition magnetic field of the order of ≳12 μG. The unusually hard spectral index from the “Head” region challenges classical particle acceleration processes and points to particle injection and reacceleration in the subrelativistic SS 433 jet, as seen in blazars and pulsar wind nebulae.