It was generally recognized that Congress had no authority to prohibit alcohol without the Eighteenth Amendment. Yes, it was technically the Volstead Act that did it, but the Eighteenth Amendment was the specific grant of authority allowing Congress to enact the Volstead Act.It didn't take it, necessarily. But that's just how it happened.
Also worth noting that while the amendment itself (notably passed by Congress then ratified by a vast majority of States) had no real teeth to regulate and enforce prohibition; the Volstead Act is what actually put Prohibition into place.
Where did Congress get the parallel authority to ban marijuana?