Els, who held both the second and third-round leads, posted a 3-under 69 to finish the tournament at 18-under-par 270. He defeated Bjorn, who shot a 68 on Sunday, by a single stroke at Mount Juliet Conrad.
This was Els' first victory on either the PGA Tour or European Tour, where he put a stranglehold on the top spot in the Order of Merit, since the Memorial in May.
He came so close in this season's major championships. Phil Mickelson holed the 18-footer to beat Els by a shot at the Masters, and then the South African lost a playoff to Todd Hamilton at the British Open. Els was two back on Sunday at the U.S. Open, but imploded with a final-round 80. Quietly, Els missed the playoff at the PGA Championship by one stroke.
Els may not have captured a major this season, but this World Golf Championships event boasts one of the strongest fields all year. The win moved Els past Tiger Woods into second on the Official World Golf Ranking.
'It's been a good summer but a tough summer, and this really caps it off for me,' said Els, who pocketed $1.2 million for the win. 'I've been chasing Tiger for the last five, six years, and now it seems like I've got to chase Vijay. I think the game is on, well and truly. Vijay has won eight times, I've won four times. So it's kind of interesting.'
Els picked up his third PGA Tour win this season and his 15th all time. On the European Tour, this was the Big Easy's second win in 2004 and the 17th of his career.
David Howell, who played in Sunday's final group with Els and Bjorn, only managed a 1-under 71, but took a solo third at 13-under-par 275.
Woods, the two-time defending champion, who also won in 1999, fought through serious back pain all week and netted a top-finish. He shot his third consecutive 2-under 70 to came in ninth at minus-10, but fell to third in the rankings for the first time in five years.
Woods has not won a stroke-play tournament since this event last year. He captured the WGC-Accenture Match Play Championship earlier this season, but now has gone a calendar year without a traditional win.
'So be it. Then I'll go into the next year,' said Woods, who skirted rumors he is getting married this week in Barbados. 'It was a long week. I'm happy to actually have played all four rounds. Somehow, I don't know how I did it, but I got a top-10 out of it.'
Light rain fell consistently on Sunday, the wind was up and temperatures fell. There was talk of a possible Monday finish because the forecast was so bad, but play was completed, albeit under difficult conditions.
Els, who held a two-shot lead heading into the final round, and Bjorn did their best from the first hole to make this a two-man race. Bjorn nearly holed his approach at the first and was assured a tap-in birdie. Els ran home a 20-foot birdie putt of his own and after Bjorn's formality, Els remained two ahead.
At the par-3 third, both players had 15 feet on opposite sides of the flag, and both made birdie. Bjorn, who served as one of European Ryder Cup captain Bernhard Langer's assistant captains two weeks ago at Oakland Hills, birdied the fifth to get within one.
Els extended the margin back to two with a birdie at the par-5 10th, but Bjorn rebounded with a birdie at the par-3 11th. Bjorn dropped a shot at 14, but reclaimed the lost stroke with a birdie at 15 to hang one shot back.
At the par-5 17th, Bjorn reached the green in two, although 65 feet from the hole. His eagle putt ran 10 feet past the hole and he missed the birdie try. Els came up short with his second, but pitched to 6 feet for his third and rolled in the birdie putt to back up by two.
Els' approach landed in a greenside bunker at the difficult closing hole at Mount Juliet, but blasted out to 15 feet. Bjorn had a 40-foot look at birdie to keep the pressure on Els, but when he missed, Els two-putted for bogey and the win.
'Thomas kept me on my toes right to the last shot,' said Els. 'It was a very tough day, but right now I'm so happy.'
Despite not making it to the winner's circle, Bjorn has to be happy as well. He walked off the course the last time he played in Ireland, the European Open, in disgust about the status of his game.
'I'm disappointed, but obviously proud of what I've done this week,' said Bjorn. 'Thinking back on the last six or seven months, I mean, this is a massive improvement. I'm just happy with being in this situation.'
Darren Clarke holed out for eagle on the first hole en route to a 4-under 68. He shared fourth place with his Ryder Cup teammate Sergio Garcia, who carded a 2-under 70 on Sunday. The duo finished at 12-under-par 276.
Local favorite Padraig Harrington posted a disappointing 1-over 73 in the final round, but tied for sixth with some good company. Reigning U.S. Open champion Retief Goosen (72) and this year's British Open winner Todd Hamilton (73) joined Harrington at minus-11.
Woods came in at minus-10, followed by Zach Johnson, who shot a final-round 71 to take 10th at 9-under-par 279.