At first, this may seem obvious. The source is Genesis 9:4 -
"Only flesh with the life thereof, which is the blood thereof, shall ye not eat."
Put in other words -
"But you must not eat meat with its lifeblood [still] in it."
But note that the phrase, "ever min hachai" is not found in this Torah passage. The verse says -
אַךְ־בָּשָׂ֕ר בְּנַפְשׁ֥וֹ דָמ֖וֹ לֹ֥א תֹאכֵֽלוּ
Even more interesting, is that it actually means something different. By a simple reading of the verse, this command is kept if the blood of the is removed from the meat. The best way to accomplish this is kosher slaughter, cutting the arteries and pouring the blood on the ground. Noah knew about clean and unclean animals and had just offered a sacrifice. So it wouldn't even be a stretch to suggest the verse is talking about draining the blood from *an animal before eating it.
"Ever min hachai" takes the meaning of the verse in a completely different direction, specifically prohibiting consumption of meat removed from a live animal.
So where does this law the rabbis include in the Noahide Laws come from? Was this law formed in such a way as to address a specific pagan practice they wanted to discourage?
*I originally wrote "...it wouldn't even be a stretch to suggest the verse is talking about draining the blood from a /-kosher-/ animal before eating it." This is INCORRECT. It is crystal clear in the previous verse that God permitted Noah to eat ALL living things. I was reflecting on God's pleasure with Noah's offering and had been researching kosher slaughter, and tried to make a connection that wasn't there. I wanted to leave the "kosher" in there and strike it through, but I couldn't figure out how to do it.