Hearthpwn

Here is the decklist I used to beat Heroic Zinaar.

The concept is simple:

Delay the game enough by using AoE cards like Flamestrike, Blizzard and Explosive Sheep to keep his board clear.

Benefit from the Freeze and Taunt mechanic to delay damage. Combo cards like Frost Nova and Doomsayer. The boss will spawn more minions on his turn regardless of having a Doomsayer on the board.

He will eventually burn all his cards. Once this happens, it's GG. He will pick up two cards per turn because of his hero power, and burn all his health.

Here is a video of my win: 

 Check out my other decks for the League of Explorers bosses:

Wing 1: Heroic Zinaar          Heroic Phaerix          Heroic Temple Escape

Wing 2: Heroic Scarvash         Heroic Mine Cart          Heroic Archaedas

Wing 3: Heroic Slitherspear        Heroic Giantfin        Heroic Lady Naz'jar

Wing 4: Heroic Skelesaurus Heroic Steel Sentinel Heroic Rafaam  Heroic Rafaam Unleashed