We investigate the properties of young (¹108 yr) M33 star clusters from the samples presented in the Ðrst two papers of this series using far-UV photometry. Previously, UBV colors were used to derive cluster ages, luminosities, and masses, assuming an extinction interpolated from neighboring stars. Fifteen of 44 clusters imaged in the Hubble Space T elescope WFPC2 with the F170W Ðlter are detected. The far-UV magnitudes provided by this Ðlter are used to rederive young cluster ages by comparing integrated photometry with stellar evolutionary models. Overall, we Ðnd ages consistent with those from our second paper from UBV photometry. However, the addition of the F170W Ñux provides three major improvements over previous work : (1) This band is more sensitive to the temperature range of clusters younger than D108 yr. (2) UBV colors for young clusters with contaminated V -band Ñuxes (from red supergiants or from line emission by surrounding excited gas) provide only an upper age limit. The addition of the far-UV Ñux allows us to extract precise ages. (3) Far-UV Ñux helps to constrain cluster extinction.New theoretical ratios are presented for cluster ages between 4 ] 106 and 1010 yr and metallicities M/L V of (Z \ 0.02, Y \ 0.28), (Z \ 0.008, Y \ 0.25), (Z \ 0.004, Y \ 0.24), (Z \ 0.001, Y \ 0.23), and (Z \ 0.0004, Y \ 0.23), extracted from the recent models of C. Chiosi. These values are used to M/L V estimate cluster masses from derived ages and measured luminosities. We Ðnd young clusters to have masses in the range 6 ] 102È2 ] 104These values are smaller than the most massive old clusters in M33 M _ . (which have masses up to a few times 105 in the sample presented in our second paper. M _ ) ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ