Watson finished at 15-under-par 198 for a two-stroke advantage after 54 holes. He has held at least a share of the lead since Thursday's first round.
Watson is looking for his fifth PGA Tour victory and first since taking the 2012 Masters.
Kevin Stadler carded a 4-under 67 on the Stadium Course at TPC Scottsdale, grabbing sole possession second place at 13-under.
Sharing third place at 12-under 201 were Ryan Moore (64), Harris English (69) and Hideki Matsuyama (68).
McPhee, Cokas 'working on their marriage' after affair
Duggar sisters unveil Christian dating rules in new book