In both the Biblical story of Genesis and the Epic of Gilgamesh we find a story of the decline of humanity from an idyllic state to our current mortal state. In both cases this decline is attributed to offending one or more gods.
The two narratives, however, follow a different path. Adam and Eve initially are immortal, and as we read through the book of Genesis we discover how they lost their immortality. In the case of Gilgamesh, the hero is very long-lived, but not himself immortal. After the death of his friend Enkidu, Gilgamesh undertakes a quest in which he travels to obtain immortality, which is possessed by Utnapishtim and is a gift of the gods. Humans are not by nature immortal by can be made immortal if the gods will it.
Utnapishtim tells the story of humans angering the gods and the gods sending a great flood, during which only Utnapishtim and his wife were spared, a story that bears obvious similarity to that of Noah.
Although Gilgamesh fails the test Utnapishtim sets him, Utnapishtim does tell Gilgamesh of a plant that can restore lost youth. Gilgamesh finds the plant, but puts it down briefly and it is stolen by a serpent, ending Gilgamesh's chance of becoming immortal. The agency of a serpent is also a similarity to the Biblical account, although Gilgamesh's serpent is just a snake, not a devil in disguise.