A method for repairing a diseased or damaged section of an aorta (i) introduces an intraluminal directing device from a remote access site to a location within a prosthesis at a target site in an aorta where the diseased or damaged section exists, the intraluminal directing device including a deflectable distal region; (ii) establishes a path to a desired fastening site on the prosthesis by manipulating the intraluminal directing device within the prosthesis to orient the distal region with respect to the desired fastening site; (iii) introduces from an intraluminal fastener applier, that is introduced along the path established in (ii), at least one tissue-piercing fastener into tissue at the desired fastening site to anchor the prosthesis; (iv) establishes a path to a different desired fastening site on the prosthesis by manipulating the intraluminal directing device within the prosthesis to orient the distal region with respect to the different desired fastening site; (v) introduces from an intraluminal fastener applier, that is introduced through the path established in (iv), at least one tissue-piercing fastener into tissue at the different desired fastening site to further anchor the prosthesis; and (vi) repeats (iv) and (v) until a desired plurality of tissue-piercing fasteners are introduced into tissue to anchor the prosthesis.