Leishman, whose only PGA Tour win came at the 2012 Travelers Championship, mixed eight birdies with two bogeys on the heavily tree-lined layout to finish a stroke in front of American Ryan Moore, South African Charl Schwartzel and England's Justin Rose.
"I feel like I've been playing pretty well for the last few months at least, and the results have been fairly good," Leishman, who tied for fifth at the British Open 11 days ago, told reporters. "I drove the ball well. It makes this course a lot easier when you're on the fairway. It's pretty tough when you're playing from the rough," said the 30-year-old, who has recorded top-11 finishes in three of his last four PGA Tour starts.
Italian Francesco Molinari, Americans Patrick Reed and Rickie Fowler and Canadian Graham DeLaet opened with 67s in the third World Golf Championships (WGC) event of the year.
Most eyes, however, were focused on former world number one Woods, who has compiled an astonishing record of success at Firestone and romped to victory last year by seven shots.
PROGRESS SHOWN
Though still tournament rusty after spending much of this season recovering from back surgery, he was satisfied with the progress shown in his game after carding six birdies, two bogeys and a double at the par-four ninth.
"I hit a lot of good shots today, I hit a few not so solid but I kind of got it around a little bit," Woods told Golf Channel after covering the back nine in two-under 33.
"Every time I dropped a shot, I got it right back the very next hole so bouncing back like that feels nice. It's just progress. I just need to get (repetitions) in.
"Coming (back) off surgery, it takes time. (My form) has been building and today was a lot better."
Woods, who missed the cut at last month's Quicken Loans National and finished 69th at the British Open in his only two events since his surgery in late March, said his strategy had been very simple in the opening round.
"You've just got to keep making birdies out here, keep the ball in play," he smiled. "It's soft right now and you can see a lot of guys under par.
"With the wind cropping up this afternoon, not a lot of guys went low but it certainly was gettable," said Woods, who double-bogeyed the ninth after missing the fairway to the right off the tee and hitting tree branches with his second shot.
Australian world number one Adam Scott, second-ranked Northern Irishman Rory McIlroy, who clinched his third major title at the British Open earlier this month, and Masters winner Bubba Watson opened with matching 69s.
Among those who did not fare well in the first round at Firestone were U.S. Open champion Martin Kaymer of Germany, who struggled to a 77, and former British Open winner Louis Oosthuizen of South Africa, who carded a 75.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Steve Keating/Frank Pingue)
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