The key is in the timing. It feels as though your sneak skill doesn't matter so much, but rather your timing. What you do is you grab all, talk to Elijah, then walk to the first generator thingy to the right of the vault door. Elijah will come through a doorway and you have to circle the generator to avoid him. Once you're on the side of the generator OPPOSITE the vault door you came from, you stop. Here, you wait until Elijah accesses a terminal. When he does, you just stand up and walk through the door he came from. If done correctly, he'll just barely miss shutting the door on you.