Well for one, introduce scrying. In Magic the Gathering, there are cards that let you look into the top however many cards of your deck, and rearrange them in the order of your choosing. The closest we have is Tracking, which is one class, and forces you to discard two of your three cards, which blows.

For second, lower the powerful effects of legendaries that breed archetypes and turn them into epics. Having less powerful effect placed on one card and doubling the amount of that card in the deck means it's less punishing to not draw the card and you're twice as likely to draw the card.

For third, stop designing cards that are amazing to play on curve and really shit off curve. Less cards like Patches, Small Time Buccaneer, Totem Golem when it was a relevant problem. These cards have created the highest failure rate built into most decks in Hearthstone history. It used to be only Rogue had this type of built in failure rate based off "Will I draw Gadget in time", now even if you run a dragon deck, with like 8 dragons in your deck, you have a real chance to not draw a dragon at all when you need them and you just flat out lose.

So there's 3 things: Add scrying, make some legendaries epics and make them less powerful doubling your consistency and lowering your power swings, and make less power swings cards that are garbage when not played perfectly on curve or with the perfect conditions and setup in your hard so there's just overall less power swings emphasized by the card drawing mechanic.