A method of closing a puncture in a blood vessel wall, including: positioning a suture placement device in a tissue tract and into a puncture in the blood vessel wall, the placement device having a length of suture with a first end, a second end and a bight between the first and second ends with the bight being prearranged on the device to define a pre-tied knot when the first end of the suture passes through the bight; advancing the first end of the length of suture in a distal direction from the device through a first penetration in the blood vessel wall adjacent to the puncture; guiding the suture length from the first penetration across a proximal side of the puncture to a second penetration adjacent to the puncture opposite the first penetration; and advancing the suture length in a proximal direction through the second penetration, through the device, and through the bight so that the two ends of the suture length are accessible external to the tissue tract for securing the suture across the puncture to close the puncture.