Watson began the day four shots off the pace but he made nine birdies and an eagle at the TPC-Doral course to give himself a chance for his first PGA Tour victory since last year's stop in New Orleans. He has three wins on the circuit.
Tiger Woods improved his opening-day score by five shots with a 67 but he was still seven shots off the pace in a tie for 15th place. World No. 1 Rory McIlroy was at 142 following a 69 and Phil Mickelson reached the tournament's midway point at 143 with a 71.
Watson's eagle came at the par-5 sixth hole, where he reached the green in two and holed a 6-foot putt. His only bogey came at the par-3 fourth.
"This golf course doesn't really suit me," Watson said. "It's tough. I'm not a big fan of No. 18 (a 467-yard, par-4 with water down the left side). I normally play it really bad. But I've played it in 1-under so far."
Jason Dufner, who shared the first-round lead with Scott, shot a 72 that left him in a tie for 10th place at 138.