After looking at my Cactus Of Arizona book, I've come to the conclusion that it is a senita cactus. Although also a night bloomer like the night blooming cereus, it was eliminated because this plant was on a cactus type plant. The night blooming cereus plant is more stick like with the blooms at the tips.
Regardless of the identification, it is a quite showy flower. Guessing it appeals to bats for pollination since it is a night bloomer.