That left Watney with an overall tally of 26 points after 36 holes in the only event on the PGA Tour which uses the Modified Stableford scoring system.
"I gotta keep going," Watney, a five-times winner on the U.S. circuit, told reporters after recording three birdies in his last eight holes. "We've got a long way to go. I'll just try to keep my head down and stay focused on where I'm at."
Former U.S. Open champion Geoff Ogilvy of Australia was alone in second place, after carding a 70, with American Wes Roach (69) in third, on 22 points.
New Zealand's Tim Wilkinson (71) and American Tommy Gainey (68) were tied for fourth on 21 points.
Under the scoring system, points are awarded on each hole for being under par, with birdies earning a player two points and eagles five. A bogey costs a player one point, double bogeys and worse three points. No points are won or lost with par.
Watney would normally be competing this week in the elite WGC-Bridgestone Invitational in Akron, Ohio but, with his world ranking having slipped to 80th, he failed to qualify for that 76-man event for the first time since 2008.
He has not triumphed on the PGA Tour since the 2012 Barclays tournament but put himself in prime position to push on for victory over the weekend in Reno after racking up a record equaling 18 points with his 63 in the opening round.
"Well, I feel like 18 (points is) good," said Watney, who held a two-point lead overnight. "I'm definitely proud of that round yesterday. I played great.
"On this golf course ... there are some scoreable holes but there are also a few really tough ones, so anything over five or six points is a good day."
Watney's 18-point tally on Thursday tied the tournament record set by American Jonathan Byrd in the final round last year.
Seventy-five players made the cut, which fell on eight points, with former major winners Lucas Glover, Todd Hamilton, Davis Love III and John Daly among those failing to advance.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Peter Rutherford)
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