A low-profile access port for subcutaneous implantation within the body of a patient is disclosed. The access port includes a receiving cup that provides a relatively large subcutaneous target to enable a catheter-bearing needle to access the port without difficulty. In addition, the access port includes a valve/seal assembly to permit pressurized fluid injection through the port while preventing backflow. In one embodiment, therefore, a low-profile access port comprises a body including a conduit with an inlet port at a proximal end thereof, and a receiving cup. The receiving cup is concavely shaped to direct a catheter-bearing needle into the conduit via the inlet port. The receiving cup is oriented substantially toward a skin surface when subcutaneously implanted within the patient to ease needle impingement thereon. A valve/seal assembly disposed in the conduit enables passage of the catheter therethrough while preventing fluid backflow.