Els -- a three-time Dubai winner and the leader after Saturday's third round -- closed with a 1-under 71, and was the runner-up at 18-under 270.
Woods made a late rush with birdies on four of the final six holes to shoot 3-under 69. He was tied for third place with Sweden's Niclas Fasth (68) at 17-under 271.
"I came so close in Sweden two years ago when I lost in a playoff for the Scandinavian Masters," said Stenson, who has made Dubai his home. "This is my second home, so to be able to win in front of family and friends is just unbelievable."