We present a spectroscopic determination of the redshift of the second source in the Jackpot gravitational lens system J0946 + 1006, for which only a photometric estimate of zphot = 2.41 +0.04 −0.21 has previously been available. By visually inspecting an archival Very Large Telescope (VLT) X-Shooter observation, we located a single emission line from the source in the H-band. Among the possible options, we find that this line is most likely to be [O III] 5007 Å at zspec = 2.035. Guided by this proposal, we were able to detect the faint C III] 1907,1909 Å emission doublet in a deep VLT Multi Unit Spectroscopic Explorer datacube. The C III] emission is spatially coincident with the brightest parts of the second Einstein ring, and strongly supports the redshift identification. The spectroscopic redshift is only marginally consistent with the photometric estimate. Re-examining the cosmological constraints from J0946 + 1006, the revised measurement favours less negative values of the dark energy equation-of-state parameter w; when combined with a cosmic microwave background prior, we infer w = −1.04 ± 0.20. The revised redshift does not significantly help to reconcile the small discrepancy in the image positions for the even more distant third source in J0946 + 1006.