The 46-year-old Mediate, looking for his first PGA Tour victory in eight years, made the eagle on the 426-yard hole a day after a hole-in-one on the par-3 third hole. He had a 13-under 129 total on the CordeValle Golf Club course in the Fall Series event.
Ryudi Imada (67) was second, and Dean Wilson (64) and David Duval (65) followed at 9 under.
U.S. Ryder Cup player Rickie Fowler shot a 65 to join Tim Herron (67), Will MacKenzie (68), Henrik Stenson (67) and Bo Van Pelt (68) at 8 under.
Mediate had eagles in consecutive rounds for the first time since 2001.
“It is just weird,” Mediate said. “A lot of stuff is happening. When that went in, I was ‘Really?’ I was pleased, but shocked.”
Mediate, for years troubled by back problems, was slightly on edge because of his 7:20 a.m. tee time, concerned that he couldn’t get loose in the cold.
“I was a little nervy to start because I was concerned the morning might be chilly,” Mediate said. “I don’t do well in the cold. But it wasn’t too bad. I hit a couple of putts and got some momentum.”
Mediate birdied four of his first 12 holes before his eagle, which made up for a later bogey.
“That was my record by miles, 34 holes without a bogey,” Mediate said. “I was so disappointed, but how could I be that angry? I wanted to go at least 36 holes. I actually tried to bogey the ninth hole too.”
Mediate said he took a putting lesson from Lee Trevino in May, and it has made a huge difference in his results.
“I spent four or five hours with him and learned so much about moving the ball to the right,” Mediate said. “It was priceless. I didn’t want to leave. Him and I are the same; we’re nuts.”
Wilson said he took advantage of smoother greens, birdieing six of eight holes at one point, recovering nicely from an early bogey.
“I think there is a lot of danger out there,” Wilson said. “I need to drive the ball well, get it on the fairway. The greens were nice and smooth in the morning, versus yesterday when they were a little bumpy.”
Duval said he played consistently well in the second round.
“I wasn’t real close to a bogey,” he said. “I felt like I hit the ball pretty well. I had a few mistakes but I came here and have gotten into a rhythm so far.”
Fowler birdied four of his final five holes to move into the top five.
“I drove the ball better,” Fowler said. “Rocco set the pace and I needed to stay with the pace. I think I did that.”
Defending champion Troy Matteson missed the cut, following his opening 72 with a 76.
The tournament, the third of five Fall Series events, is in its first year at CordeValle Golf Club after three seasons at Grawhawk in Scottsdale, Ariz.