Second-ranked Scheffler shot a three-under 68 in front of some 200,000 fans at TPC Scottsdale on Saturday to get to 13 under, two strokes ahead of world No.3 Jon Rahm and Nick Taylor.
Australia's former world No.1 Jason Day is on track for a second consecutive top-10 finish and has a shot at a drought-breaking victory, sitting tied sixth, four shots behind Scheffler after a 68.
Spanish star Rahm also had a 68, holing a curling 40-footer for birdie on the stadium 16th hole for his third birdie in four holes. American Taylor shot 67.
Scheffler would take the No.1 spot from Rory McIlroy - tied for 28th at three under after a 70 - with a victory, as long as McIlroy finishes worse than solo third.Â
Scheffler also could get to No.1 by finishing solo second if McIlroy is 36th or worse and Rahm doesn't win.
Rahm would go to No.1 with a victory if McIlroy finishes worse than a three-way tie for second, or by finishing solo second if McIlroy finishes worse than solo 47th and Scheffler doesn't win.
Jordan Spieth and Adam Hadwin were at 10 under while Day was tied at nine under with Rickie Fowler, the 2019 winner, who had a 67,Tyrrell Hatton (67), Sungjae Im (67), and Xander Schauffele (70).
Speith had the best score in the delayed second round, finishing off a 63 in the morning. He added a 69 in the third round, highlighted by a 77-yard bunker shot to three feet to set up a birdie on the par-4 17th.
Last year, Scheffler beat Patrick Cantlay here in a playoff for his first PGA Tour title. Scheffler added victories in the Arnold Palmer Invitational, WGC-Match Play and Masters and was the PGA Tour's player of the year.
The 26-year-old Texan followed a bogey on the par-5 13th - his first bogey since his fourth hole Thursday - with a birdie on the par-4 14th, hitting a 210-yard shot to 4 feet. He also birdied the 17th.
Rahm opened the year with consecutive victories in the Sentry Tournament of Champions and The American Express.
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