Watson birdied four straight holes on the back nine. Mickelson, beginning his round on the back nine, rallied after being 2-over through six holes.
Akron -- Phil Mickelson closed his first round of the WGC-Bridgestone Invitational with a flourish, notching birdies on six of his last 12 holes to finish with a 4-under par 66.
Bubba Watson, like Mickelson a left-handed golfer, fired a 64 on Firestone's famed South Course and holds a two-stroke lead over Mickelson and Kenny Perry, who carded a 66.
Tiger Woods, a seven-time winner of the tournament and looking for his first win of the season, has begun his round with bogeys on No. 1 and No. 2, and his playing No. 3.
Masters champion Mickelson has a chance this week to surpass Woods and achieve the world's No. 1 ranking for the first time in his career. Lefty began play on Firestone's back nine, and was 2-over after bogeys on Nos. 14 and 15.
Mickelson birdied the 667-yard, par-5 16th hole. Then, on his back nine, he strung together birdies on hole Nos. 2, 3, 6, 7 and 9.
Watson set up his sterling round with birdies on the 11th through 14th holes.
Chad Campbell and Sean O'Hair shot 3-under 67s. Steve Stricker, Gregory Bourdy of France and Rory McIlroy of Ireland completed their rounds at 2-under, 68. In the clubhouse at 1-under par 69 are Ernie Els of South Africa, Alexander Noren of Sweden and Matt Kuchar.
Players off to good starts include Canadian left-hander Mike Weir, who is 3-under par after four holes, and Bo Van Pelt at 3-under after six. Sweden's Peter Hanson has played seven holes at 2-under, and Australia's Adam Scott is 2-under through five holes.
British Open champion Louis Oosthuizen of South Africa shot a 2-over 72, and U.S. Open champ Graeme McDowell of Ireland just began, parring his first hole.