An implantable access port for use in transferring a fluid transdermally between an external fluid storage or dispensing device and a site within a patient's body is disclosed. The access port includes a base, a bowl-shaped reservoir defined within the base by a smooth surfaced wall, and a septum secured to the base and enclosing the reservoir within the base. The access port also includes a reservoir outlet defined centrally within the reservoir. The bowl-shaped reservoir is defined by a continuous smooth-surfaced curvilinear wall. The reservoir may thus be sized and shaped as a parabola, or may be hemispherical or semi-hemispherical in cross-section. The reservoir outlet is defined at a center point on the bottom of the reservoir wall, may be partially or fully recessed within the bottom of the reservoir wall, and is also defined in the base tangentially with respect to the bottom of the reservoir wall. The access port also has an outlet passageway defined within the base and extending in communication with the reservoir outlet and an external opening defined in the exterior of the base.