The Englishman had eight birdies in his second consecutive bogey-free round at Amata Spring Country Club to reach 20 under overall.
Westwood had 10 birdies and an eagle in the first round Thursday.
“Arguably a better round this morning than yesterday in windy conditions!” Westwood tweeted. “64 to add to yesterday’s 60. For sure the best I’ve ever played. -20.”
John Daly followed his opening-round 65 with a 73 to slip to fourth at 6 under, 14 shots adrift of Westwood.
“I’ll try to keep the lead irrelevant and keep on playing as I’ve been playing,” Westwood said. “I’m playing pretty well and I want to maintain that and keep making birdies and no bogeys.”
Schwartzel eagled the 15th and had six birdies, but bogeyed the 8th and 12th. He acknowledged that he only has a slim chance of catching Westwood.
“I feel like Lee is playing his own tournament and we are playing something else,” he said. “Halfway through it now, I still feel like I’ve got a very outside chance.”
British Open champion Darren Clarke, Sergio Garcia and Ryo Ishikawa all narrowly made the cut at 3 over but Thailand’s top-ranked player Thongchai Jaidee retired after 13 holes Friday because of a back injury.