Hearthpwn

To clarify, I did not beat Rafaam on my first try, but I did beat him on the first try with this deck.

After struggling for a day or so with net decks on Rafaam, I ended up making something fairly similar to a budget control deck.  Basically, if you have the building blocks for a control priest already, just go all in on removal.  Things like Cabal Shadow Priest + Shrinkmeister can be good to steal some handy cards (I stole a Grommash with it), but they can be swapped out.  The only epic I'd say is a must  have is the BGH to give you just one more big removal. He could be subbed with a second cobra, but you have to be able to protect it until your turn comes back around.

While not as flashy as Ysera or Alex, Chromaggus won me this fight on the first try with this deck.  The RNG gods gave me my second Entomb with him on the board as well as a Mind Control, so Rafaam couldn't keep any of the big nasties on his side of the board.

As for the artifacts, I held the one that deals three damage to everything until he filled the board with zombies.  If you don't have one of those available, Shadow Madness and Mind Control Tech can help you thin the herd.

Mulligan for at least one of your big removals.  My mulligan for my run was SW:P, SW:D, and Emperor Cobra.

Good luck.  Have fun!