A hot beverage brewing apparatus. A pressurized hot liquid delivery system provides liquid under pressure within a range of acceptable brewing temperatures without any mechanical pump. Water is apportioned into sealable tank volumes, one of which is heated to boil the liquid and produce steam under pressure. The pressurized steam displaces the liquid from the tank volumes in proportion and at a temperature that is within the acceptable brewing range. The hot liquid under pressure is directed to a capsule receiving station to infuse a material in a capsule. The capsule dispenses the brewed beverage without contacting the brewing apparatus.