If Nidalee enters combat against a unit, and the opponent uses Sacrifice on their unit in that showdown, do I still draw from Nidalee?

Yes, you will still draw from Nidalee, Cat Form, provided she remains on the battlefield after combat and you are declared the winner.

Explanation

According to Nidalee's ability, she triggers when she "wins a combat," which is defined as "remaining after combat."

When your opponent uses Sacrifice on their unit, that unit is sent to the trash as a cost (Rule 357). Because that unit is no longer on the battlefield during the Combat Cleanup phase (when combat results are determined), your Nidalee is effectively the only unit remaining at the battlefield.

Sequence of Events

1. Combat Damage Step: Combat damage is dealt. If your opponent's unit is not destroyed by combat damage, it remains on the battlefield.
2. Sacrifice Reaction: In response to something (or during the showdown), your opponent plays Sacrifice. The unit is killed as a cost and moved to the trash before Sacrifice even resolves.
3. Battlefield State: Because the opponent's unit has been removed from the battlefield, your Nidalee remains at the battlefield alone.
4. Combat Cleanup: The game determines the winner. Since your Nidalee remains at the battlefield and the opponent’s unit does not, Nidalee meets her win condition.
5. Trigger: Her ability triggers ("When I win a combat, draw 1"), and you draw a card.

Even though the opponent’s unit died due to Sacrifice rather than combat damage, the outcome is the same regarding the win condition: Nidalee "remained" at the battlefield after combat, and the opposing player's units did not.

This is my interpretation based on Rule 461.3 and the logic established in FAQ #10248 regarding combat results. No official FAQ exists for this specific interaction with Sacrifice.