Amongst the chasing pack included former phenom Ryo Ishikawa, who carded the round of the day with a nine-under 63 to sit two shots back, while Lee Westwood is alongside Fox a further shot back.
A solid final round will lift Fox out of a relative slump, with the 31-year-old having not claimed a top 25 finish since September.
Fox is also set to retain his status as New Zealand's number one golfer, after Danny Lee missed the cut at the Phoenix Open.
Lee carded a two-under 69 to move to even par on the tournament, but it wasn't enough as he missed the cut by just one shot. Like Fox, he has also been struggling for form of late, having failed to record a top-25 since November.
The high-profile American duo of Rickie Fowler and Bryson DeChambeau lead at 10-under. Fowler has had a lot of success at the TPC Scottsdale course, without winning. He finished a shot behind Hunter Mahan in 2010, lost to Hideki Matsuyama on the fourth extra hole in 2016, and tied for fourth last year.
"From the first couple times I played it, I knew it was just kind of a matter of time before I would win here," Fowler said. "I know I can win here. I put myself in position plenty of times."
The tournament lost some star power when Jordan Spieth missed the cut and two-time defending champion Matsuyama withdrew because of a left wrist injury.
The third-ranked Spieth last failed to advance to weekend play in May, when he missed consecutive cuts in The Players Championship and the AT&T Byron Nelson. Matsuyama's injury ended his bid to match Arnold Palmer's event record of three straight victories.
Elsewhere, Kieran Muir is the best of the New Zealanders at the Victorian Open on the Australian PGA Tour.
Muir carded a superb seven-under 65 to shoot into a share of sixth with one round remaining – just three shots behind Australian leader Simon Hawkes.
Ben Campbell shot a three-under 69 to move inside the top 10 at five-under, where he is tied with Nick Voke, who slid backwards after a two-over 74.
Ryan Chisnall (17th) and Gareth Paddison (21st) are the only other New Zealanders in the top 40.
- With AP
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