Harrington eagled the 17th hole and finished at 3-over 283 four shots ahead of Englishman Ian Poulter, who also closed with a 69 for 287.
Fifty-three-year-old Australian Greg Norman, who held the lead halfway through the final round, fell to a 7-over 77 to tie for third place with Swede Henrik Stenson (71) at 9-over 289.
"When you shoot in the 60s in that sort of wind, you've got to pleased on a day like today," Harrington said. "I was real good today. I had my mind in the right place."
Norman, who has not won on the PGA Tour in 11 years and seldom enters tour events now, had four bogeys on the back nine, ending his chances.
The "Shark" was trying to become the oldest golfer to win a Grand Slam tournament.
" I would have loved to have won, no kidding about that," Norman said. "I know it was a good week. Can I walk away feeling down? Of course, I can. But can I walk away feeling pretty good? Yeah, I can do that as well."
Amateur Chris Wood of England (71) and American Jim Furyk (72) shared fifth place at 10-over 290.