The 50-year-old Mediate, the Allianz Championship winner in February in his first Champions Tour start, followed his opening 8-under 63 with a 64 to reach 15 under at tree-lined Canyon Meadows.
"I'm going to need to go 4-, 5- or 6-under par easy to win this golf tournament tomorrow," Mediate said. "It's good to be where I am. I like the feeling. I want to go play the third round right now, but you can't do that. I just want to get to the first tee and get going."
He had seven birdies on the back nine after making an eagle and two bogeys on the front side.
"I didn't really play that bad on the front nine," Mediate said. "On the back nine, the gates they opened right up."
Bobby Clampett was second after a 65.
"I was just really trying to hang in there," Clampett said. "I wasn't playing particularly well early on in the round and missed a couple shots — tee shot at 7 and a tee shot at 9 — and managed to squeak out a couple bogeys on those holes. I just hung in there a made some good putts today."
Tom Pernice Jr., David Frost and Michael Allen were 11 under. Pernice had a 64, and Frost and Allen shot 66.
"Today was a good day to get me closer to the lead, so I'm within striking distance," Pernice said. "I'm going to have to play good again tomorrow though."
Jay Don Blake matched the tour record with three eagles en route to a 66 that left him at 10 under along with Kirk Triplett (66), Jeff Sluman (68) and Bart Bryant (68).
Mike Goodes was in the group at 9 under after matching Mediate's course record with a 63.
"I was walking down the last few holes saying if you can't have fun doing this, you can't have any fun, so I was enjoying it," said Goodes, who had eight birdies in his bogey-free round. "It was a great round and I got in position where I can have a really good tournament."
Fred Couples was 8 under after a 65.
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