Yang carded a 3-under 69 to win the event at 14-under-par 274, two shots better than Woods, who posted a 5-under 67 and finished second here for the second year in a row.
Goosen had control of the championship, but played horribly on the back nine. He played the second side in 3-over 39 en route to a 1-over 73 and a share of third place with Campbell, who fired a 64 on Sunday. The pair of former U.S. Open winners finished at 11-under-par 277.
Goosen birdied the second and third holes to move two ahead, but Yang held his ground and holed a 7-foot par save on the fifth to stay two behind. Goosen missed several makeable birdie tries on the rest of his front side, but Yang flew past him late on the front nine.
Yang missed the green at the par-3 sixth, but chipped in for birdie. He joined Goosen in a tie for the lead when he holed a putt from off the green at seven, then moved in front when his 10-footer fell into the cup at eight. Goosen had a similar putt, but failed and that would be all Yang needed.
Goosen hit a terrible approach at the 10th that sailed long and left. He pitched his second to 25 feet, but could not convert the par putt. Goosen drove into a bunker at the 11th and three-putted for a bogey to suddenly fall three behind Yang.
The 34-year-old four-time winner on the Japan Golf Tour padded his advantage at the par-3 12th when he stuffed his tee ball to 2 feet. Yang tapped in the short birdie putt and was four in front.
Goosen got within three with a birdie at 14, but gave the shot right back at 15 when he missed the fairway, then the green and failed to convert a 4- footer for par.
Yang made things interesting down the stretch. At the short, par-4 16th, Yang drove against a board and his second came up short of the putting surface. He chipped to 20 feet and nearly drained the par putt, but the ball hopped out. Yang bogeyed the hole, but still had a three-shot cushion.
Yang hit into a bunker at the par-3 17th and blasted out to 10 feet. His par putt stayed above ground, meaning the lead was down to two, but Woods was now a factor.
The reigning British Open and PGA champion birdied 14, 16 and 18 to get into the clubhouse at minus-12, which was the same score Goosen stood at on the 18th tee.
Goosen drove into the left rough and cost himself any chance of getting on in two. Yang also missed the fairway and both players laid up short in the fairway. Goosen chunked his third into the water, allowing Yang to play more conservatively. Yang knocked his third almost 50 feet past the hole.
Goosen hit his fifth to 10 feet and made the bogey putt. Yang rolled his birdie putt 8 feet past the hole, but rolled in the par save to collect his first win on the European Tour.
'I wasn't nervous at all, but the last three holes I couldn't get it on the green, then I got nervous,' Yang said through a translator. 'I feel like I'm up in the air. I can't grasp it in words.'
Marc Warren hit the stick with his third at the last, but the ball rolled all the way off the green. He made bogey for a 1-under 71 and a solo fifth at minus-10.
Paul Casey (71), Padraig Harrington (70) and Robert Karlsson (70) shared sixth place at minus-8.
First and second-round leader Jyoti Randhawa struggled on Sunday. He only managed a 3-over 75 and tied for ninth with K.J. Choi (70), Johan Edfors (70), Francesco Molinari (72) and world No. 2 Jim Furyk (68). The group finished at 7-under-par 281.