Walker, who clinched his fourth PGA Tour victory at the Sony Open in January, picked up shots at the sixth, seventh and eighth before ending his round with a comfortable par at the ninth to post a six-under total of 138.
Australian Aaron Baddeley (71) and American Charley Hoffman (72) were tied at five under, a stroke better than world number six Jordan Spieth (69) and fellow American Kevin Na (68).
"I hit a couple of good shots in there and just kept trying to build on each hole there at the end," San Antonio resident Walker told Golf Channel. "That was a nice little finish.
"I've been working hard on my putting at home and it was ready to go this week. It feels like the hard work is paying off.
"There should be a lot of support from friends and family so it's going to be fun," Walker said of his thoughts heading into the weekend. "I look forward to the challenge."
The players had struggled in strong gusts up to 40 mph (64 kph) on Thursday when the average score was just under 77, but on Friday the wind died down and switched direction.
"It played completely different," said Spieth, who won the Valspar Championship 12 days ago in his most recent PGA Tour start.
"Yesterday was a whipping north wind and today was kind of a little calmer out of the south-west. I'm very happy. I made some good clutch par saves. I needed them today and yesterday.
"To be at four under on a course that's this challenging and be two back, you couldn't ask for much more right now."
Five-times major champion Phil Mickelson, who has not won on the PGA Tour since the 2013 British Open, was among a group of five players at two under after shooting a 72.
The cut fell at six-over 150 with U.S. Open champion Martin Kaymer and fellow former major winners Lucas Glover and Geoff Ogilvy among those failing to advance.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Gene Cherry)
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