Woods closed with a 3-under 69, sweeping his arm when the final putt dropped, then slamming down his first in a celebration that was a long time coming. It had been 749 days and 26 official tournaments since he last won on Nov. 15, 2009 at the Australian Masters, back when he looked as though he would rule golf as long as he played.

But he crashed his car into a fire hydrant outside his Florida home on Thanksgiving night, and shocking revelations of extramarital affairs began to emerge, which eventually led to a divorce. Since then, he has changed swing coaches and endured more injuries, missing two majors this summer and missing the cut in another.

Now, however, it looks clear that Woods is on an upward path.

This was his 83rd win worldwide, and the fifth time he has captured the Chevron World Challenge, which he hosts for his foundation. Woods finished at 10-under 278 and donated the $1.2 million to his foundation.

The win moved him from No. 52 to No. 21 in the world ranking, and likely will send expectations soaring for 2012. Woods will not play again until starting his year in Abu Dhabi at the end of January.

Asked if the emotion was joyous, satisfying or simply relief, Woods smiled and said, ``It just feels awesome whatever it is.''

He had a worthy adversary in Johnson, who had a one-shot lead going into the final round and trailed for only three holes. Johnson tied Woods with a birdie on the par-5 13th, made an unlikely par on the 14th by chipping from the bottom of the green, and appeared to seize control by holing a 12-foot birdie putt on the 16th hole.

Johnson thought his birdie putt on the 17th was good all the way until it burned the edge of the cup. Woods, running out of time, drained his birdie putt to force a tie and send the tournament to the 18th.

Woods also was tied on the 18th at Sherwood a year ago and stuffed his approach into 3 feet. Graeme McDowell holed a 20-foot putt to force a playoff, and beat Woods on the first extra hole.

Johnson, however, missed his birdie putt from 15 feet, leaving the stage to Woods. He hasn't been in these situations much over the last two years, but this one, finally, had a familiar ending.

Johnson closed with a 71 and still took home $650,000 for the holidays. Paul Casey, who opened with a 79, had his third straight round in the 60s to finish alone in third at 5 under.

``Tiger can have a long career,'' Casey said when he finished. ``We might look back in another 10 years and actually forget about the last couple of years.''

Woods had a four-shot lead over McDowell a year ago, a margin that evaporated quickly when Woods showed early signs of a struggle, particularly with a pair of three-putts. There was no such evidence this time.

Despite nearly driving into trouble to the right of the par-5 second, Woods escaped and hit wedge to 3{ feet for birdie. His lone bogey on the front nine came at the par-3 eighth, with a back right pin that requires a fade. Woods tugged it well left of the green, and his pitch at a 45-degree angle was too strong and rolled into the fringe about 15 feet away.

Johnson's chip on the third was too strong, he three-putted from about 35 feet for bogey on the fifth and he played a poor chip from below the eighth green for another bogey.

They were tied at the turn when Woods began to pull away. From the right rough, Woods hit a soft sand wedge that landed in the first cut short of the green and fed down the slope to about 4 feet. He two-putted from long range for birdie on the par-5 11th to stretch his lead to two shots when Johnson caught a buried lie in the bunker.

Woods bogeyed the 12th from a bunker, though, and Johnson's birdie on the 13th set up a final hour that was up for grabs until Woods came through in the clutch on the last two holes.