A search for instability of nucleons bound in Xe-136 nuclei is reported with 223 kg yr exposure of Xe136 in the EXO-200 experiment. Lifetime limits of 3.3 x 10^23 and 1.9 x 10^23 yr are established for nucleon decay to Sb133 and Te133, respectively. These are the most stringent to date, exceeding the prior decay limits by a factor of 9 and 7, respectively.