The equator crosses two continents:
Ordered by land area (largest to smallest):
Note: The equator also crosses Asia (Indonesia — islands of Sumatra, Borneo, Sulawesi, Halmahera; and territorial waters of Maldives, Kiribati). However, by standard continental definitions (landmasses), it crosses the Asian continental shelf but not the mainland. Most geographic authorities list three continents (South America, Africa, Asia) or two (excluding Asia's island portions). The question's premise ("those in order") implies two; Africa is larger than South America.