I agree, it does look like this flower but it was not blooming at night. I took this picture in daylight. Also, it was in a neighbors yard and not in the desert, but I assume such a plant can be in a yard.
It looks like a photo shown here. Maybe some open at night and the flower lasts into daylight hours. Not familiar with the many kinds. Night blooming Cereus Cactus Flower by seemyshots
Maybe Epiphyllum hookeri ? The flower is said to last 2-3 days. epiphyllum hookeri On-line Guide to the positive identification of Members of the Cactus Family