His final total was 18-under 270.
Micheel (69), the 2003 PGA Champion, finished 13-under 275.
In the final round, Woods, who played flawlessly over four days, shot a 4-under 68, recording his first bogey since the first hole on Thursday.
"This is sweet," he said. "Any time you can win a major championship under these circumstances, on this great golf course against this field, I'm very fortunate."
"Today I didn't drive the ball quite as well as I would have liked," Micheel admitted. "I'm not sure even if I would have hit every fairway, I would have been able to catch Tiger. He's too good."
Woods claimed a winner's check of $1,224,000.