South Korea's Yang got hot on his back nine, carding six birdies after the turn including on holes 17 and 18 to finish in a flurry at TPC Scottsdale, Arizona.
The big-hitting Watson started in such fashion, birdying his opening two holes and going to the turn at four under, before another four birdies plus a bogey at 11 saw him to a stellar opening round.
Strangely, the two major winners are chasing their first PGA Tour titles since winning the 2012 Masters (Watson) and the 2009 PGA Championship (Yang).
Their early buffer is slender, though, with seven players a shot back on six under - with Australians Greg Chalmers and Matt Jones the only non-Americans among them.
The Australian pair are level with Pat Perez, Kevin Stadler, William McGirt, Harris English and Chris Kirk on six under.
Then there are eight players tied for 10th on five under, most notably major winner Keegan Bradley - with Zimbabwe's Brendon de Jonge and Japan's Hideki Matsuyama the only non-locals in the group.
Last week's Farmers Insurance Open winner Scott Stallings opened his week in Arizona with a one-under 70, while defending champion Phil Mickelson shrugged off back soreness to post an even-par 71 to be tied for 65th.
Mickelson was in doubt to play this weekend due to injury, but managed to tee off at the event he has won three times.
Of the 132 players in the field, 10 failed to finish their first 18 holes - with Thailand's Kiradech Aphibarnrat the most advanced of those on the leaderboard at four under through 15.
YE Yang, Bubba Watson share Phoenix Open lead
