Akjeromy’s Silence Priest

If you’re lucky enough to draw a Northshire Cleric to start with, you can usually hit their low level minion without dying and then heal it for an extra card.

Shadow Word: Pain and Annoy-o-Tron will help you keep Northshire Cleric on the board longer to keep getting extra cards, especially if you buff him with Velen's Chosen

At this point you can steal a secret with Kezan Mystic,  destroy their weapon with Acidic Swamp Ooze, or if they manage to have a bunch of buffed low level minions out, you can silence them all with Mass Dispel and get an extra card, and/or destroy them all with Holy Nova

Sludge Belcher can come out next, or Vol'jin can steal health from one of their higher health minions

if you have time you can enhance your healing hero power with Justicar Trueheart

Entomb will mitgate their next big minion, and Lightbomb can destroy everybody, but you may have too use Confuse to make that happen

The mech bombs from Dr. Boom can disrupt divine shields and small taunts, and can make way for Ragnaros the Firelord who is always good for 8 damage somewhere, at least once before they kill him. You can even silence him with Ironbeak Owl and then he can attack directly on the next turn.

Alexstrasza is a great card. Whether you have too use her battlecry on your opponent or yourself, she evens things out quickly.