Mediate needed birdies on the last two holes to join Robert Allenby and Graeme McDowell at the end of a day filled with rainy and windy weather conditions at the difficult Royal Birkdale course in Southport, England.
"I was like everyone else, trying to survive," Mediate admitted. "All of sudden, a couple things happen. It was just survival and by no means pretty."
Three others -- 53 year-old Greg Norman, Adam Scott and Bart Bryant -- share fourth place at even-par 70.
The conditions led to enormous scores by a host of well-known veterans, including world No. 3 Geoff Ogilvy (5-over 77), Phil Mickelson (7-over 79), Ernie Els (8-over 80) and Vijay Singh (8-over 80).
The tournament's 1985 winner Sandy Lyle withdrew after playing just nine holes, making his 33rd British Open appearance the shortest of his career.
2014: The Year in Music [PHOTOS]