Rahm capped a bogey-free round with a 25-foot birdie putt that gave him a 15-under total and three-shot lead over Max Homa (69) as they duelled on Saturday.
The in-form pair had to share the spotlight with Tiger Woods who shot a 67, his lowest Saturday round in an official event since he won the Zozo Championship in Japan in late 2019 as he rose to tied 26th after scraping through the cut.
Keith Mitchell made his only bogey on the final hole and had a 69 to fall four behind in third place. The only other player within five shots of Rahm was Patrick Cantlay (68).
Lucas Herbert shot a 68 to be tied 18th as the leading Australian but a distant 11 shots from Rahm with countryman Jason Day (71) a further shot back along with Woods, Justin Thomas and others.
Rahm has been the best player in golf over the last six months. Dating to the BMW PGA Championship on the European tour, he has finished among the top 10 in nine consecutive tournaments, winning four of them.
All that's left is a return to No.1 in the world, and a victory on Sunday would ensure he overtakes Scottie Scheffler who reclaimed the top spot with his Phoenix Open just six days ago.
For Woods, it felt like a win just being back on the PGA Tour for four straight rounds, something he hasn't done since the Masters. Then again, he only played three times last year because of his right leg severely damaged in a February 2021 car crash.
He made the cut on the number when the second round was completed Saturday morning, 11 shots off the lead and started on the back nine in one of the last few groups.
That didn't keep thousands of fans lining the fairway over the next five hours.
Woods made a few birdies on the back nine, and then hit 5-iron onto the front of the green at the par-5 first hole, the ball rolling to within 3 feet of the pin for a tap in eagle.
"I wanted to get in touch with the leaders today, I was hoping to shoot something a little bit lower than I did just so I could reach out to them hopefully with a low round tomorrow," Woods said. "I might be a little far away."
That leader is Rahm, and it's daunting regardless of the margin.
Rahm was in a terrific battle with Californian Homa, who won at Riviera two years ago.
It was Homa who blinked first.
He found the fairway bunker on the 15th, the toughest hole, came up short of the green and missed a tough 10-footer for par. He pulled his tee shot on the par-3 16th into a bunker and again missed a 10-foot putt for par.
Within range for Rahm is the oldest 72-hole scoring record on the PGA Tour - 20-under 264 by Lanny Wadkins in 1985.
All that matters to Rahm is another victory that would give him the ranking that his game embodies at the moment.
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