'I ate well and slept well last night. I knew I just had to come out and shoot a good golf score (today), and the rest would take care of itself,' Howell said. 'Obviously there was a little extra pressure playing with Tiger, but it can't affect you as long as you block it out mentally.'
Nick Dougherty, who held a share of the lead after rounds one and two, closed with a 3-under 69 to share third place at 14-under-par 274. He was joined there by Nick O'Hern, who finished with a 1-over 73.
World No. 2 Vijay Singh managed a 69 on Sunday to end at minus-13, where he shared fifth place with Thomas Bjorn.
Howell led Woods by one stroke entering the round. He pushed the advantage to two strokes with a birdie on the second. Woods drained a 12-foot birdie on the third, but Howell kicked in a short birdie putt of his own on three to maintain a two-stroke lead.
'I started beautifully. I birdied the second and third,' said Howell. 'After a quick swing on the third tee, I was happy how my long game settled. I was able to pull away early on.'
The big turning point early in the round came at the fifth. Howell stuck his approach within four feet to set up birdie. Meanwhile, Woods stumbled to a three-putt bogey to drop four strokes back.
Woods knocked his second shot to 3 feet at the seventh. Howell, though, drained a 25-foot birdie try before Woods could make his birdie.
Howell missed the green short at the par-5 eighth and was unable to save his par. He three-putted for bogey at the next to slip back to 18 under and his lead was only two.
The 30-year-old managed to recover one stroke as he made an 8-foot birdie putt on the 10th. Woods, who missed makeable birdie putts at eight and 10, finally sank a 10-footer for birdie at 12 to move to minus-17.
Howell, who got a good bounce out of the rough off the tee, also birdied 12 to keep his three-stroke margin. He two-putted for par on each of the next three holes to stay three ahead.
Woods scrambled to three straight pars of his own before a poor tee shot on the 16th. The 29-year-old went for the green on the short par-4, but lost the tee shot short and right of the green in a hazard.
He took a drop and knocked his third within 6 feet, but missed the par putt to fall four back.
Howell two-putted for par on each of the last three holes to secure the win.
'My best score of the week -- a 65 on Thursday -- was when I was least happy with my game, strange game that it is,' said Howell, who was the only player to post four rounds in the 60s this week. 'Sometimes golf is like that. You do the right things and when you are not really flushing it, you just concentrate a bit more, play the percentages and that is what I did all week.
'As the week progressed, what you hope to do is try and start hitting the ball slightly better and that is exactly what happened. And when that happens, you generally have a good week.'
Woods missed a birdie try inside of 10 feet on the 17th, but did manage a two- putt birdie on the par-5 closing hole.
Paul Casey posted a 4-under 68 in the final round to end alone in seventh place at 12-under-par 276. Jean-Francois Remesy and Thaworn Wiratchant were one stroke further back at minus-11.
U.S. Open champion Michael Campbell faltered to a 1-over 73 on Sunday to take 10th place at 10-under-par 278. Former British Open winner Paul Lawrie was one stroke behind Campbell at minus-9 after back-to-back 70s on the weekend.