Yb14MnSb11 and Yb14MgSb11 are among the best p-type high-temperature (>1200 K) thermoelectric materials, yet other compounds of this Ca14AlSb11 structure type have not matched their stability and efficiency. First-principles computations show that the features in the electronic structures that have been identified to lead to high thermoelectric performances are present in Yb14ZnSb11, which has been presumed to be a poor thermoelectric material. We show that the previously reported low power factor of Yb14ZnSb11 is not intrinsic and is due to the presence of a Yb9Zn4+xSb9 impurity uniquely present in the Zn system. Phase-pure Yb14ZnSb11 synthesized through a route avoiding the impurity formation reveals its exceptional high-temperature thermoelectric properties, reaching a peak zT of 1.2 at 1175 K. Beyond Yb14ZnSb11, the favorable band structure features for thermoelectric performance are universal among the Ca14AlSb11 structure type, opening the possibility for high-performance thermoelectric materials.