Hearthpwn

Reasons to try this deck: Have you ever OTKed a Secret Mage on turn 5?

 Proof of Legend

Decklist from jjjjjj_hs who played it to #1 legend. Kudos to this guy because I've been playing Hearthstone since classic and this is by far the most powerful deck I've ever played. Wouldn't change a single card. 

Intro: Mozaki Mage is one turn kill (OTK) combo deck. The goal is to survive long enough to cast Mozaki, Master Duelist, then a bunch of spells and OTK the opponent. Ice Block and Frost Nova can buy you enough time vs. most decks. The combo can be done as early as turn 5 if you draw perfect, but turns 6 to 9 are more common.

Subs: You can use a second Ancient Mysteries if you don't have Varden Dawngrasp

Combo Turn Planning: 45 seconds is not a lot of time. Plan it out the turns before the combo. If you are going to combo on turn 7, use all the time you have on turns 5 or 6 to mentally plan the mana costs, draw, cast order, and # spells you need to cast before having having lethal. You have a lot of time early game turns to plan, but on combo turn time is limited. 

Delaying: Every turn you survive increases the likelihood of OTK. if you can delay until turn 7, 8, or 9 without risking a loss then even better! 

Mana: You need at least 2 mana discount to combo! This can be any combination of Incanter's Flow and Sorcerer's Apprentice.

Draw and spell # multiplication: Research Project, Cram Session, Refreshing Spring Water, Arcane Intellect, Conjure Mana Biscuit, Ray of Frost drastically increase spell count and keep your hand full. You need card draw to combo. At least one draw card keeps the combo going. Do not burn key cards with overdraw.

Cards:
Cram Session is your main combo extender. A few cards into your combo it will A) be free, and B) draw a bunch of cards due to spell damage on Mozaki, Master Duelist.  I would recommend doing cram session after 4 or 5 spells. Be careful not to mill yourself and die - never Cram Session deep into a combo. I have accidentally milled and killed myself with Cram Session on combo turns, always look at card # remaining in deck.

Conjure Mana Biscuit: This is what enables your turn 5 or 6 OTK. If you have used Conjure Mana Biscuit during the first 4 turns, and have a Mana Biscuit in hand, then you can drop Mozaki, Master Duelist on turn 5, Mana Biscuit, then Sorcerer's Apprentice. If you discounted your deck with Incanter's Flow at least once, then Ice Lance, Ray of Frost, Ancient Mysteries, Conjure Mana Biscuit, Incanter's Flow, Cram Session, Frostbolt, Research Project, and Runed Orb are all free. At this point you can cycle through the whole deck on same turn with draw cards. 

Refreshing Spring Water: If discounted is awesome during combo. Draw and more mana. 

Incanter's Flow: You need at least one for an early OTK.

Sorcerer's Apprentice: If possible try to have this on your combo turn and drop it after Mozaki, Master Duelist. This with Incanter's Flow is what lets you cycle through your deck for free. 

Ray of Frost: Can be used for two free spells on combo turn, or for survival before combo. This card isn't essential so use it as a cheap way to trigger cards like Counterspell and Oh My Yogg! so your more important spell aren't countered

Burn Cards: You need at least 3 burn cards (a combination of Ice Lance, Frostbolt, or Runed Orb) for lethal. Against armored opponent you may need more. A lot of times you won't have all 3 at combo start but will draw them during combo

Runed Orb: Flex card. Can be used to survive, or as a burn card. Sometimes you draw it mid combo and it adds extra damage. Make sure you select a cheap spell on the discover so you can cast that spell during combo. 

Defense cards: 

Frost Nova: Freeze the big boards. Try to waste these before wasting Ice Block if possible. Weapons and spells can still kill you so if they are in lethal range w a weapon or spell you will need an Ice Block. 

Varden Dawngrasp: Was torn on adding this card, but overall it is great vs. board based decks like Darkglare, Odd Paladin, etc. Also this card can bypass Loatheb since it isn't a spell! If you know they are going to Loatheb then save this for the turn after. Also good vs. hand disruption, makes cards like Dirty Rat less likely to hit Mozaki

Ice Block: Keeps you alive. Try to not cast this until you need it! A lot of decks run Horde Operative which can steal your Ice Block and cost you the game. Also decks with Zephrys the Great will not give anti-secret options if there is no secret in play. Delaying Ice Block until last second stops these cards from easily countering you. 

Mulligans - ALWAYS keep: Incanter's Flow, Ancient Mysteries. Can keep Conjure Mana Biscuit if you have Ancient Mysteries + Incanter's Flow
vs. Aggro (in addition to above): Ice Block, Frostbolt. 
vs. Control (in addition to above): Taelan Fordring, Mozaki, Master Duelist, Refreshing Spring Water, Arcane Intellect 

Matchups
Secret Mage: By far my most common opponent. They are favored. Always play Mozaki, Master Duelist before Sorcerer's Apprentice to avoid Explosive Runes killing you on your turn. Must kill Secret Mage quickly or you will lose. Don't let Counterspell hit Incanter's Flow or Ice Block.  Secret mage runs a single copy of Ice Block, so if you know they have it in play then leave them as close to 1hp as possible before popping it so you can lethal them turn after. In this case minimum damage combo may be better (see math at bottom), but only if you know they have Ice Block in play. Takes some experience. 
Pirate Warrior: Same as secret mage minus the secrets.
Cute Warlock: Same as secret mage minus the secrets.
Odd DH: Bad matchup, you will probably lose unless you can OTK them turn 6
LPG Mage: Pain in ass. They can Zephrys the Great a Flare, they can Loatheb, then they can Potion of Illusion and repeat it. They run Ice Block. Kill them ASAP before you get bogged down.
Reno/Highlander decks in general: You are favored but watch out for Zephrys the Great into a Flare, and for Dirty Rat. Also remember some run anti-secret tech. 
Reno Priest: Dirty Rat and Mindrender Illucia can result in almost an instant loss if they burn your combo pieces. You can't do anything to play around this, so take them out ASAP.
Darkglare Warlock/Quest Warlock: You are favored. Keep big board frozen and use ice blocks. Remember they can burst you for 16 with Power Overwhelming x4.
Odd Paladin: You are favored. Same as Darkglare. Watchout for Loatheb locking you out, and remember they can burst you for 12 to 18 with Conviction. Counter Oh My Yogg! with Ray of Frost
Big Priest: You are heavily favored. They have almost no way to win unless you don't draw Mozaki. 
Kingsbane Rogue: You are favored
Odd rogue: Watch out for Loatheb. Same as Odd DH 
Galakrond Shaman: You are favored. Watch out for Loatheb
Murloc Shaman: Same as Odd Paladin and Darkglare Warlock. Remember they can burst for high damage with Old Murk-Eye, Everyfin is Awesome, and Nofin Can Stop Us.
Control decks: You are favored and should win unless they Dirty Rat Mozaki
Celestial alignment: Have never lost to one. Save a Mana Biscuit. Once they cast Celestial Alignment, you can drop Mozaki, Master Duelist, Mana Biscuit, then Sorcerer's Apprentice. The rest of your deck is free since celestial changed cost to 1 and apprentice lowers by 1. You need a big combo to penetrate the armor (>60-70 damage) so take your time in the planning phase, they can't OTK you because of Ice Block so no rush

About to die/didn't draw the damage spells: If you have Mozaki, Master Duelist in hand and some draw you can summon him and start cycling through your deck and hope you draw the damage pieces! 

Sample Combos: These are only 5 spells combos before burn to illustrate the minimum you need for lethal in most cases. Most of your combos will be closer to 10 cards so the damage will be significantly higher (see images below for examples of real combos), at that point you don't even have to count since your damage will be way past lethal

Runic Orb + Frostbolt + Ice Lance
27 damage: 5 spells before burn, then Runic Orb for 7, Frostbolt for 9, and Ice Lance for 11.  

 Frostbolt + Frostbolt + Ice Lance: 
28 damage: 5 spells before burn, then Frostbolt for 8, Frostbolt for 9, Ice Lance for 11 

Frostbolt + Ice Lance + Ice Lance: 
29 Damage: 5 spells before burn , then Frostbolt for 8, Ice Lance for 10, and Ice Lance for 11.  

Higher damage example (vs. celestial alignment druid, odd warrior, etc.): 69 damage, 9 spells before burn, then Runic Orb for 11, Runic Orb for 12, Frostbolt for 14, Frostbolt for 15, Ice Lance for 17. This can go up easily to 90-100 damage if you cast the second Ice Lance or if the combo is bigger (I usually do around 70 to 80 vs. druid) 

More proof of concept:

Turn 6 OTK of another Secret Mage, 13 damage still in hand, 12 card combo

Turn 6 OTK of yet another Secret Mage, 38 damage still in hand, 11 card combo

Turn 7 OTK of Odd Paladin, 17 damage still in hand, 15 card combo

Turn 9 OTK of Control Warlock, 10 card combo

Then 7 OTK Darkglare Warlock

Turn 5 OTK of Darkglare Warlock 

Turn 9 OTK Reno Shaman

Turn 7 OTK Evolve Shaman (first one I've seen at legend)

Thanks to SinisterMe for allowing me to post his great video guide to Mozaki Mage (see below)!