Watson punched the air after holing an outrageous 20-yard bunker shot for eagle at the 18th to get into a playoff with South Africa's Clark at 11-under.
The left-hander then rolled in a lightning quick 25-foot putt down a slope on the same hole for the winning birdie, sparking wild celebrations for his first World Golf Championships event win and his first victory of any kind outside the US.
Leading at 12-under par with three holes to play, Watson had seemingly imploded with a bogey followed by a double-bogey at the 16th and 17th to fall to nine under.
At that point five players were a shot ahead of him, until his magic from the sand saw him finish 11-under for the tournament.
"I told my caddie walking into the bunker on 18, 'It's been a miserable couple holes here. But this will change everything if this goes in'," Watson told reporters after the win.
"He says, 'This is how legends are made.' And it actually went in. And I didn't know what to do. So I just yelled."
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